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Journal articles on the topic 'Isometrie'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 May 2024

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1

Mantovani, Lisa. "Achillessehnentendinopathie: Welchen Nutzen hat ein isometrisches Training?" MSK – Muskuloskelettale Physiotherapie 26, no. 03 (July 2022): 141–46. http://dx.doi.org/10.1055/a-1827-2679.

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Isometrisches Training wird seit ein paar Jahren zur Schmerzlinderung bei einer Achillessehnentendinopathie empfohlen. Doch nicht nur Schmerz, auch die reduzierte physische Leistungsfähigkeit sollte in der Therapie adressiert werden, da diese möglicherweise zu Rückfällen führen kann. Kann Isometrie auch die Leistungsfähigkeit beeinflussen?

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2

Jiménez-Vargas, Antonio, and María Isabel Ramírez. "Algebraic Reflexivity of Non-Canonical Isometries on Lipschitz Spaces." Mathematics 9, no. 14 (July 11, 2021): 1635. http://dx.doi.org/10.3390/math9141635.

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Let Lip([0,1]) be the Banach space of all Lipschitz complex-valued functions f on [0,1], equipped with one of the norms: fσ=|f(0)|+f′L∞ or fm=max|f(0)|,f′L∞, where ·L∞ denotes the essential supremum norm. It is known that the surjective linear isometries of such spaces are integral operators, rather than the more familiar weighted composition operators. In this paper, we describe the topological reflexive closure of the isometry group of Lip([0,1]). Namely, we prove that every approximate local isometry of Lip([0,1]) can be represented as a sum of an elementary weighted composition operator and an integral operator. This description allows us to establish the algebraic reflexivity of the sets of surjective linear isometries, isometric reflections, and generalized bi-circular projections of Lip([0,1]). Additionally, some complete characterizations of such reflections and projections are stated.

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3

Sun, Yuqi. "On Coarse Isometries and Linear Isometries between Banach Spaces." Axioms 13, no. 3 (February 28, 2024): 157. http://dx.doi.org/10.3390/axioms13030157.

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Let X,Y be two Banach spaces and f:X→Y be a standard coarse isometry. In this paper, we first show a sufficient and necessary condition for the coarse left-inverse operator of general Banach spaces to admit a linearly isometric right inverse. Furthermore, by using the well-known simultaneous extension operator, we obtain an asymptotical stability result when Y is a space of continuous functions. In addition, we also prove that every coarse left-inverse operator does admit a linear isometric right inverse without other assumptions when Y is a Lp(1<p<∞) space, or both X and Y are finite dimensional spaces of the same dimension. Making use of the results mentioned above, we generalize several results of isometric embeddings and give a stability result of coarse isometries between Banach spaces.

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4

BAKHIT, M. A. "ISOMETRIES ON SOME GENERAL FAMILY FUNCTION SPACES AMONG COMPOSITION OPERATORS." Journal of Mathematical Analysis 13, no. 1 (March 30, 2022): 1–13. http://dx.doi.org/10.54379/jma-2022-1-1.

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In this paper, we discuss the isometries of composition operators on the holomorphic general family function spaces F(p, q, s). First, we classify the isometric composition operators acting on a general Banach spaces. For 1 < p < 2, we display that an isometry of Cφ is caused only by a rotation of the disk. We scrutinize the previous work on the case for p ≥ 2. Also, we characterize many of the foregoing results about all α-Besov-type spaces F(p, αp − 2, s), α > 0. We exhibit that in every classes F(p, αp − 2, s) except for the Dirichlet space D = F(2, 0, 0), rotations are the only that produce isometries.

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Mahmoud, Sid, Muneo ChO, and Ji Lee. "(m,q)-isometric and (m,∞)-isometric tuples of commutative mappings on a metric space." Filomat 34, no. 7 (2020): 2425–37. http://dx.doi.org/10.2298/fil2007425m.

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In this paper, we introduce new concepts of (m,q)-isometries and (m,?)-isometries tuples of commutative mappings on metrics spaces. We discuss the most interesting results concerning this class of mappings obtained form the idea of generalizing the (m,q)-isometries and (m,?)-isometries for single mappings. In particular, we prove that if T = (T1,..., Tn) is an (m,q)-isometric commutative and power bounded tuple, then T is a (1,q)-isometric tuple. Moreover, we show that if T = (T1,...,Td) is an (m,?)- isometric commutative tuple of mappings on a metric space (E,d), then there exists a metric d? on E such that T is a (1,?)-isometric tuple on (E,d?).

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6

Popov, Vladimir A. "Locally Isometric Riemannian Analytic Spaces." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 4-1 (216-1) (December 28, 2022): 55–64. http://dx.doi.org/10.18522/1026-2237-2022-4-1-55-64.

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Classes of locally isometric Riemannian analytic manifolds are studied. A generalization of the concept of completeness is given. We consider the Lie algebra 𝔤 of all Killing vector fields of a Riemannian analytic manifold, its stationary subalgebra 𝔥 the simply connected Lie group 𝐺 corresponding to the Lie algebra 𝔤, and the subgroup 𝐻 corresponding to the Lie subalgebra 𝔥. In the absence of a center in the algebra 𝔤 the concept of a quasi-complete (compressed) manifold is introduced. An oriented Riemannian analytic manifold whose vector field algebra has zero center is said to be quasi-complete if it is non-extendable and does not admit non-trivial orientation-preserving and all Killing vector fields local isometries to itself. The main property of such a manifold is that it is unique in the class of all locally isometric Riemannian analytic manifolds, and any locally given isometry of this manifold 𝑀 into itself can be analytically extended to an isometry 𝑓: 𝑀 ≈ 𝑀. For an arbitrary class of locally isometric Riemannian analytic manifolds, a definition of a pseudocomplete manifold is given, which is complete if a complete manifold exists in the given class. A Riemannian analytic simply connected manifold M is called pseudocomplete if it has the following properties. 𝑀 is non-extendable. There is no locally isometric covering map f; M→N, where N is a simply connected Riemannian analytic manifold and f (M) is an open subset of N not equal to N.

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7

Aleman, Alexandru, Peter Duren, María J. Martín, and Dragan Vukotić. "Multiplicative Isometries and Isometric Zero-Divisors." Canadian Journal of Mathematics 62, no. 5 (October 1, 2010): 961–74. http://dx.doi.org/10.4153/cjm-2010-048-7.

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AbstractFor some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.

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8

Li, Chi-Kwong. "Norms, Isometries, and Isometry Groups." American Mathematical Monthly 107, no. 4 (April 2000): 334. http://dx.doi.org/10.2307/2589178.

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9

Li, Chi-Kwong. "Norms, Isometries, and Isometry Groups." American Mathematical Monthly 107, no. 4 (April 2000): 334–40. http://dx.doi.org/10.1080/00029890.2000.12005201.

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10

Cima, Joseph A., and Warren R. Wogen. "Isometric equivalence of isometries on $H^p$." Proceedings of the American Mathematical Society 144, no. 11 (April 27, 2016): 4887–98. http://dx.doi.org/10.1090/proc/13106.

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11

Dyshko, Serhii. "Isometry groups of combinatorial codes." Journal of Algebra and Its Applications 17, no. 06 (May 23, 2018): 1850114. http://dx.doi.org/10.1142/s0219498818501141.

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Two isometry groups of combinatorial codes are described: the group of isometries, that is, the group of Hamming isometries from a code to itself and the group of monomial isometries, which is the group of those isometries of a code to itself that extend to monomial maps. Unlike the case of classical linear codes, where these groups are the same, it is shown that for combinatorial codes the groups can be arbitrarily different. In particular, there exist codes with the richest possible group of isometries and the trivial group of monomial isometries. In the paper, the two groups are characterized and codes with predefined isometry groups are constructed.

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12

Rassias, Themistocles M. "Isometries and approximate isometries." International Journal of Mathematics and Mathematical Sciences 25, no. 2 (2001): 73–91. http://dx.doi.org/10.1155/s0161171201004392.

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13

MENDES, MIGUEL, and MATTHEW NICOL. "PERIODICITY AND RECURRENCE IN PIECEWISE ROTATIONS OF EUCLIDEAN SPACES." International Journal of Bifurcation and Chaos 14, no. 07 (July 2004): 2353–61. http://dx.doi.org/10.1142/s0218127404010813.

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We consider the behavior of piecewise isometries in Euclidean spaces. We show that if n is odd and the system contains no orientation reversing isometries then recurrent orbits with rational coding are not expected. More precisely, a prevalent set of piecewise isometries do not have recurrent points having rational coding. This implies that when all atoms are convex no periodic points exist for almost every piecewise isometry. By contrast, if n≥2 is even then periodic points are stable for almost every piecewise isometry whose set of defining isometries are not orientation reversing. If, in addition, the defining isometries satisfy an incommensurability condition then all unbounded orbits must be irrationally coded.

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14

Chō, Muneo, Ji Lee, and Haruna Motoyoshi. "On [m,C]-isometric operators." Filomat 31, no. 7 (2017): 2073–80. http://dx.doi.org/10.2298/fil1707073c.

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In this paper we introduce an [m;C]-isometric operator T on a complex Hilbert space H and study its spectral properties. We show that if T is an [m,C]-isometric operator and N is an n-nilpotent operator, respectively, then T + N is an [m + 2n ? 2,C]-isometric operator. Finally we give a short proof of Duggal?s result for tensor product of m-isometries and give a similar result for [m,C]-isometric operators.

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15

Bloom, Walter R., and Martin E. Walter. "Isomorphisms of hypergroups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 52, no. 3 (June 1992): 383–400. http://dx.doi.org/10.1017/s1446788700035102.

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AbstractLet K1, K2 be locally compact hypergroups. It is shown that every isometric isomorphism between their measure algebras restricts to an isometric isomorphism between their L1-algebras. This result is used to relate isometries of the measure algebras to homeomorphisms of the underlying locally compact spaces.

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16

Jung, Soon-Mo. "Hyers-Ulam stability of isometries on bounded domains." Open Mathematics 19, no. 1 (January 1, 2021): 675–89. http://dx.doi.org/10.1515/math-2021-0063.

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Abstract More than 20 years after Fickett attempted to prove the Hyers-Ulam stability of isometries defined on bounded subsets of R n {{\mathbb{R}}}^{n} in 1981, Alestalo et al. [Isometric approximation, Israel J. Math. 125 (2001), 61–82] and Väisälä [Isometric approximation property in Euclidean spaces, Israel J. Math. 128 (2002), 127] improved Fickett’s theorem significantly. In this paper, we will improve Fickett’s theorem by proving the Hyers-Ulam stability of isometries defined on bounded subsets of R n {{\mathbb{R}}}^{n} using a more intuitive and more efficient approach that differs greatly from the methods used by Alestalo et al. and Väisälä.

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17

Arias, Jeanine Concepcion H., and Manuel Joseph C. Loquias. "Similarity isometries of point packings." Acta Crystallographica Section A Foundations and Advances 76, no. 6 (October 19, 2020): 677–86. http://dx.doi.org/10.1107/s2053273320011547.

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A linear isometry R of {\bb R}^{d} is called a similarity isometry of a lattice \Gamma\subseteq{\bb R}^{d} if there exists a positive real number β such that βRΓ is a sublattice of (finite index in) Γ. The set βRΓ is referred to as a similar sublattice of Γ. A (crystallographic) point packing generated by a lattice Γ is a union of Γ with finitely many shifted copies of Γ. In this study, the notion of similarity isometries is extended to point packings. A characterization for the similarity isometries of point packings is provided and the corresponding similar subpackings are identified. Planar examples are discussed, namely the 1 × 2 rectangular lattice and the hexagonal packing (or honeycomb lattice). Finally, similarity isometries of point packings about points different from the origin are considered by studying similarity isometries of shifted point packings. In particular, similarity isometries of a certain shifted hexagonal packing are computed and compared with those of the hexagonal packing.

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18

Malvetti, Emanuel, Raban Iten, and Roger Colbeck. "Quantum Circuits for Sparse Isometries." Quantum 5 (March 15, 2021): 412. http://dx.doi.org/10.22331/q-2021-03-15-412.

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We consider the task of breaking down a quantum computation given as an isometry into C-NOTs and single-qubit gates, while keeping the number of C-NOT gates small. Although several decompositions are known for general isometries, here we focus on a method based on Householder reflections that adapts well in the case of sparse isometries. We show how to use this method to decompose an arbitrary isometry before illustrating that the method can lead to significant improvements in the case of sparse isometries. We also discuss the classical complexity of this method and illustrate its effectiveness in the case of sparse state preparation by applying it to randomly chosen sparse states.

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19

SKALSKI, ADAM, and JOACHIM ZACHARIAS. "WOLD DECOMPOSITION FOR REPRESENTATIONS OF PRODUCT SYSTEMS OF C*-CORRESPONDENCES." International Journal of Mathematics 19, no. 04 (April 2008): 455–79. http://dx.doi.org/10.1142/s0129167x08004765.

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Higher-rank versions of Wold decomposition are shown to hold for doubly commuting isometric representations of product systems of C*-correspondences over [Formula: see text], generalizing the classical result for a doubly commuting pair of isometries due to Słociński. Certain decompositions are also obtained for the general, not necessarily doubly commuting, case and several corollaries and examples are provided. Possibilities of extending isometric representations to fully coisometric ones are discussed.

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20

SZENTHE, J. "ISOMETRY HORIZONS IN SPHERICALLY SYMMETRIC SPACE–TIMES." International Journal of Geometric Methods in Modern Physics 03, no. 05n06 (September 2006): 1263–71. http://dx.doi.org/10.1142/s0219887806001582.

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Some event horizons in space–times that are invariant under an isometric action, considered first by Carter, are called isometry horizons, especially Killing horizons. In this paper, isometry horizons in spherically symmetric space–times are considered. It is shown that these isometry horizons are all Killing horizons.

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21

Botelho, Fernanda, and Dijana Ilisevic. "On isometries with finite spectrum." Journal of Operator Theory 86, no. 2 (November 15, 2021): 255–73. http://dx.doi.org/10.7900/jot.2020apr11.2270.

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In this paper we investigate inverse eigenvalue problems for finite spectrum linear isometries on complex Banach spaces. We establish necessary conditions on a finite set of modulus one complex numbers to be the spectrum of a linear isometry. In particular, we study periodic linear isometries on the large class of Banach spaces X with the following property: if T:X→X is a linear isometry with two-point spectrum {1,λ} then λ=−1 or the eigenprojections of T are Hermitian.

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22

Ogur, Oguz, and Zekiye Gunes. "A Note on non-Newtonian Isometry." WSEAS TRANSACTIONS ON MATHEMATICS 23 (February 6, 2024): 80–86. http://dx.doi.org/10.37394/23206.2024.23.10.

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In this article, we introduce non-Newtonian isometry and examine some of its basic properties. We also give a characterization of the relationship between real isometry and non-Newtonian isometry. Finally, we show that the ν−measure of ν−measurable sets is invariant for every generator under ν−isometries.

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23

Ahmed, Ahmed. "Higher dimensional [m,C]-isometric commuting d-tuple of operators." Filomat 36, no. 12 (2022): 4173–84. http://dx.doi.org/10.2298/fil2212173a.

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In this paper we recover an [m,C]-isometric operators and (m,C)-isometric commuting tuples of operators on a Hilbert space studied respectively in [11] and [16], we introduce the class of [m,C]-isometries for tuple of commuting operators. This is a generalization of the class of [m,C]-isometric commuting operators on a Hilbert spaces. A commuting tuples of operators S = (S1,..., Sp) ? B(H)p is said to be [m,C]-isometric p-tuple of commuting operators if ?m (S,C):= ?m j=0 (?1)m?j (m j) (? |?|=j j!/?! CS?CS?)=0 for some positive integer m and some conjugation C. We consider a multi-variable generalization of these single variable [m,C]-isometric operators and explore some of their basic properties.

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24

Rocha, Roberio Pereira, and Maria Deusa Ferreira da Silva. "Uma Revisão Sistemática Abordando o Tangram, o GeoGebra e as Opções de Isometria do Plano." Educação Matemática Pesquisa : Revista do Programa de Estudos Pós-Graduados em Educação Matemática 23, no. 1 (April 11, 2021): 741–68. http://dx.doi.org/10.23925/1983-3156.2021v23i1p741-768.

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ResumoEste artigo apresenta os resultados de parte uma pesquisa de mestrado, e tem como objetivo mapear e analisar pesquisas publicadas de 2015 até 2020, realizadas em nível de ensino básico sobre a utilização do Tangram, GeoGebra e opções de isometria do plano no ensino da matemática. A metodologia utilizada foi a revisão sistemática de literatura, e partiu de buscas de artigos e dissertações realizadas nos periódicos da Biblioteca Digital Brasileira de Teses e Dissertações (BDTD), no Banco de Teses e Dissertações da CAPES e no Google Acadêmico. Usamos as duplas de descritores GeoGebra/Tangram, Tangram/Matemática e GeoGebra/Isometrias e localizamos 293 pesquisas. Após a seleção, guiada fielmente pelo protocolo estabelecido na revisão sistemática, consideramos dez estudos como amostra final da revisão. Concluímos que os trabalhos analisados apontam para a importância da variação de metodologias e utilização de recursos como GeoGebra e Tangram para potencializar o ensino de matemática. A pesquisa evidenciou a significativa contribuição do GeoGebra como incentivador do interesse dos alunos pelo estudo das isometrias do plano. Além disso, constatamos a importância do Tangram utilizado conjuntamente com o GeoGebra como facilitador da apropriação dos conceitos geométricos, instigador da curiosidade, propulsor da criatividade e mediador da percepção espacial. Todavia, percebemos a existência de uma lacuna nesse rol de estudos. Não encontramos estudos que utilizassem simultaneamente estes três elementos: GeoGebra, Simetria e Tangram. E é nessa nova perspectiva, a partir dessa lacuna, que estamos organizando esta pesquisa, ou seja, à luz da teoria da atividade, queremos investigar as estratégias matemáticas dos alunos envolvidos nessas construções de isometrias, durante a formação das figuras do Tangram no ambiente do GeoGebra.Palavras-chave: GeoGebra, Ensino básico, Tangram.AbstractThis article presents the results of part of a master’s research and aims to map and analyse research published from 2015 through 2020 at basic education level on the use of Tangram, GeoGebra and options of isometry of the plane in mathematics teaching. The methodology used was the systematic literature review and started from searches for articles and theses carried out in the journals of the Biblioteca Digital Brasileira de Teses e Dissertações/Brazilian Digital Library of Theses and Dissertations (BDTD), CAPES Banco de Teses e Dissertações/Thesis and Dissertations Bank, and Google Acadêmico/ Google Scholar. We used the pairs of descriptors GeoGebra/Tangram, Tangram/Mathematics and GeoGebra/Isometries and found 293 studies. After the selection, guided faithfully by the protocol established in the systematic review, we considered ten studies as the final sample of the review. We concluded that the works analysed point to the importance of varying methodologies and using resources such as GeoGebra and Tangram to enhance mathematics teaching. The research showed the significant contribution of GeoGebra as an incentive for the student's interest in studying the isometries of the plane. In addition, we note the importance of the Tangram used together with GeoGebra as a facilitator of the appropriation of geometric concepts, an instigator of curiosity, a propeller of creativity, and a mediator of spatial perception. However, we perceived a gap in this list of studies. We did not find studies that used these three elements simultaneously: GeoGebra, Simetria, and Tangram. It is from this new perspective, from this gap, that we are organising this research, i.e., in the light of the theory of activity, we want to investigate the mathematical strategies of the students involved in those isometric constructions, during the formation of the Tangram figures in the environment of the GeoGebra.Keywords: GeoGebra, Basic education, Tangram.ResumenEste artículo presenta los resultados de parte de una investigación de maestría y tiene como objetivo mapear y analizar investigaciones publicadas desde 2015 hasta 2020 en nivel de educación básica sobre el uso de Tangram, GeoGebra y opciones de isometría del plano en la enseñanza de las matemáticas. La metodología utilizada fue la revisión sistemática de la literatura y partió de búsquedas de artículos y tesis realizadas en las revistas de la Biblioteca Digital Brasileira de Teses e Dissertações (BDTD), Banco de Teses e Dissertações de CAPES y Google Académico. Utilizamos los pares de descriptores GeoGebra/Tangram, Tangram/Matemáticas y GeoGebra/Isometrías y encontramos 293 estudios. Tras la selección, guiados fielmente por el protocolo establecido en la revisión sistemática, consideramos diez estudios como muestra final de la revisión. Concluimos que los trabajos analizados apuntan a la importancia de variar metodologías y utilizar recursos como GeoGebra y Tangram para potenciar la enseñanza de las matemáticas. La investigación mostró la importante contribución de GeoGebra como incentivo al interés del estudiante por estudiar las isometrías del plano. Además, notamos la importancia del Tangram utilizado junto con GeoGebra como facilitador de la apropiación de conceptos geométricos, instigador de la curiosidad, propulsor de la creatividad y mediador de la percepción espacial. Sin embargo, percibimos una brecha en esta lista de estudios. No encontramos estudios que utilizaran estos tres elementos simultáneamente: GeoGebra, Simetria y Tangram. Es desde esta nueva perspectiva, desde esta brecha, que estamos organizando esta investigación, es decir, a la luz de la teoría de la actividad, queremos investigar las estrategias matemáticas de los estudiantes involucrados en esas construcciones isométricas, durante la formación de las figuras de Tangram en el entorno de GeoGebra.Palabras clave: GeoGebra, Educación básica, Tangram

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FU, XI, and XIANTAO WANG. "ISOMETRIES AND DISCRETE ISOMETRY SUBGROUPS OF HYPERBOLIC SPACES." Glasgow Mathematical Journal 51, no. 1 (January 2009): 31–38. http://dx.doi.org/10.1017/s0017089508004503.

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AbstractLet n be the n-dimensional hyperbolic space with n ≥ 2. Suppose that G is a discrete, sense-preserving subgroup of Isomn, the isometry group of n. Let p be the projection map from n to the quotient space M = n/G. The first goal of this paper is to prove that for any a ∈ ∂n (the sphere at infinity of n), there exists an open neighbourhood U of a in n ∪ ∂ n such that p is an isometry on U ∩ n if and only if a ∈ oΩ(G) (the domain of proper discontinuity of G). This is a generalization of the main result discussed in the work by Y. D. Kim (A theorem on discrete, torsion free subgroups of Isomn, Geometriae Dedicata109 (2004), 51–57). The second goal is to obtain a new characterization for the elements of Isomn by using a class of hyperbolic geometric objects: hyperbolic isosceles right triangles. The proof is based on a geometric approach.

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26

Bermúdez, Teresa, Antonio Martinón, Vladimir Müller, and Juan Agustín Noda. "Perturbation ofm-Isometries by Nilpotent Operators." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/745479.

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We prove that ifTis anm-isometry on a Hilbert space andQann-nilpotent operator commuting withT, thenT+Qis a2n+m-2-isometry. Moreover, we show that a similar result form, q-isometries on Banach spaces is not true.

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LANG, URS. "INJECTIVE HULLS OF CERTAIN DISCRETE METRIC SPACES AND GROUPS." Journal of Topology and Analysis 05, no. 03 (August 25, 2013): 297–331. http://dx.doi.org/10.1142/s1793525313500118.

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Injective metric spaces, or absolute 1-Lipschitz retracts, share a number of properties with CAT(0) spaces. In the '60s Isbell showed that every metric space X has an injective hull E (X). Here it is proved that if X is the vertex set of a connected locally finite graph with a uniform stability property of intervals, then E (X) is a locally finite polyhedral complex with finitely many isometry types of n-cells, isometric to polytopes in [Formula: see text], for each n. This applies to a class of finitely generated groups Γ, including all word hyperbolic groups and abelian groups, among others. Then Γ acts properly on E(Γ) by cellular isometries, and the first barycentric subdivision of E(Γ) is a model for the classifying space [Formula: see text] for proper actions. If Γ is hyperbolic, E(Γ) is finite dimensional and the action is cocompact. In particular, every hyperbolic group acts properly and cocompactly on a space of non-positive curvature in a weak (but non-coarse) sense.

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28

Molnár, Lajos. "2-LOCAL ISOMETRIES OF SOME OPERATOR ALGEBRAS." Proceedings of the Edinburgh Mathematical Society 45, no. 2 (June 2002): 349–52. http://dx.doi.org/10.1017/s0013091500000043.

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AbstractAs a consequence of the main result of the paper we obtain that every 2-local isometry of the $C^*$-algebra $B(H)$ of all bounded linear operators on a separable infinite-dimensional Hilbert space $H$ is an isometry. We have a similar statement concerning the isometries of any extension of the algebra of all compact operators by a separable commutative $C^*$-algebra. Therefore, on those $C^*$-algebras the isometries are completely determined by their local actions on the two-point subsets of the underlying algebras.AMS 2000 Mathematics subject classification: Primary 47B49

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DING, GUANG-GUI, and JIAN-ZE LI. "ISOMETRIES BETWEEN UNIT SPHERES OF THE -SUM OF STRICTLY CONVEX NORMED SPACES." Bulletin of the Australian Mathematical Society 88, no. 3 (March 28, 2013): 369–75. http://dx.doi.org/10.1017/s000497271300018x.

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AbstractWe prove that any surjective isometry between unit spheres of the ${\ell }^{\infty } $-sum of strictly convex normed spaces can be extended to a linear isometry on the whole space, and we solve the isometric extension problem affirmatively in this case.

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30

Koldobsky, Alexander. "Isometric Stability Property of Certain Banach Spaces." Canadian Mathematical Bulletin 38, no. 1 (March 1, 1995): 93–97. http://dx.doi.org/10.4153/cmb-1995-012-9.

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AbstractLet E be one of the spaces C(K) and L1, F be an arbitrary Banach space, p > 1, and (X, σ) be a space with a finite measure. We prove that E is isometric to a subspace of the Lebesgue-Bochner space LP(X; F) only if E is isometric to a subspace of F. Moreover, every isometry T from E into Lp(X; F) has the form Te(x) = h(x)U(x)e, e ∊ E, where h: X —> R is a measurable function and, for every x ∊ X, U(x) is an isometry from E to F

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31

Lilian, Anyembe, Musundi Sammy Wabomba, and Kinyanjui Jeremiah Ndung’u. "On Unitary Quasi-equivalence and Partial Isometry Operators in Hilbert Spaces." Journal of Advances in Mathematics and Computer Science 38, no. 10 (October 18, 2023): 113–20. http://dx.doi.org/10.9734/jamcs/2023/v38i101829.

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Unitary quasi-equivalence has been shown to be an equivalence relation. Similarly, unitary quasi-equivalence has been proven to preserve normality, hyponormality and binormality of operators. However, the properties of unitary quasi-equivalence and partial isometric operators have not been established. In this paper therefore, the study aims to determine the properties of unitary quasi-equivalence and isometry, co-isometry and partial isometry operators.

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32

Gal, Nadia J., and James Jamison. "Isometries and isometric equivalence of hermitian operators on A1,p(X)." Journal of Mathematical Analysis and Applications 339, no. 1 (March 2008): 225–39. http://dx.doi.org/10.1016/j.jmaa.2007.06.045.

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33

Camerlo, Riccardo, Alberto Marcone, and Luca Motto Ros. "On isometry and isometric embeddability between ultrametric Polish spaces." Advances in Mathematics 329 (April 2018): 1231–84. http://dx.doi.org/10.1016/j.aim.2018.03.001.

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34

Loquias, Manuel Joseph C., and Peter Zeiner. "The coincidence problem for shifted lattices and crystallographic point packings." Acta Crystallographica Section A Foundations and Advances 70, no. 6 (October 24, 2014): 656–69. http://dx.doi.org/10.1107/s2053273314016696.

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A coincidence site lattice is a sublattice formed by the intersection of a lattice Γ in {\bb R}^d with the image of Γ under a linear isometry. Such a linear isometry is referred to as a linear coincidence isometry of Γ. The more general case allowing any affine isometry is considered here. Consequently, general results on coincidence isometries of shifted copies of lattices, and of crystallographic point packings are obtained. In particular, the shifted square lattice and the diamond packing are discussed in detail.

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35

Novinger, W. P., and D. M. Oberlin. "Linear Isometries of some Normed Spaces of Analytic Functions." Canadian Journal of Mathematics 37, no. 1 (February 1, 1985): 62–74. http://dx.doi.org/10.4153/cjm-1985-005-3.

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For 1 ≦ p < ∞ let Hp denote the familiar Hardy space of analytic functions on the open unit disc D and let ‖·‖ denote the Hp norm. Let Sp denote the space of analytic functions f on D such that f′ ∊ Hp. In this paper we will describe the linear isometries of Sp into itself when Sp is equipped with either of two norms. The first norm we consider is given by(1)and the second by(2)(It is well known [1, Theorem 3.11] that f′ ∊ Hp implies continuity for f on D, the closure of D. Thus (2) actually defines a norm on Sp.) In the former case, with the norm defined by (1), we will show that an isometry of Sp induces, in a sense to be made precise in Section 2, an isometry of Hp and that Forelli's characterization [2] of the isometries of Hp can thus be used to describe the isometries of Hp.

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36

HULL, C. M. "COMPLEX STRUCTURES AND ISOMETRIES IN THE (2, 0) SUPERSYMMETRIC NON-LINEAR SIGMA MODEL." Modern Physics Letters A 05, no. 22 (September 10, 1990): 1793–800. http://dx.doi.org/10.1142/s0217732390002043.

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A study is made of those (2,0) supersymmetric non-linear sigma-models which are invariant under the action of an isometry group; this class includes the (2,0) supersymmetric Wess-Zumino-Novikov-Witten models. If, as in the case of the WZNW model, some of the isometries are not holomorphic, then those isometries do not commute with the second supersymmetry and closing the algebra appears to give an infinite number of supersymmetries. It is shown that if any non-holomorphic isometry is accompanied by a compensating deformation of the complex structure, then the symmetry algebra closes without the need to introduce any new symmetries, enabling the model, together with all its symmetries, to be formulated in (2,0) superspace.

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37

GROFF, BRADLEY W. "QUASI-ISOMETRIES, BOUNDARIES AND JSJ-DECOMPOSITIONS OF RELATIVELY HYPERBOLIC GROUPS." Journal of Topology and Analysis 05, no. 04 (December 2013): 451–75. http://dx.doi.org/10.1142/s1793525313500192.

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We demonstrate the quasi-isometry invariance of two important geometric structures for relatively hyperbolic groups: the coned space and the cusped space. As applications, we produce a JSJ-decomposition for relatively hyperbolic groups which is invariant under quasi-isometries and outer automorphisms, as well as a related splitting of the quasi-isometry groups of relatively hyperbolic groups.

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38

Wood, Jay A. "Isometry groups of additive codes over finite fields." Journal of Algebra and Its Applications 17, no. 10 (October 2018): 1850198. http://dx.doi.org/10.1142/s0219498818501980.

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When [Formula: see text] is a linear code over a finite field [Formula: see text], every linear Hamming isometry of [Formula: see text] to itself is the restriction of a linear Hamming isometry of [Formula: see text] to itself, i.e. a monomial transformation. This is no longer the case for additive codes over non-prime fields. Every monomial transformation mapping [Formula: see text] to itself is an additive Hamming isometry, but there may exist additive Hamming isometries that are not monomial transformations.The monomial transformations mapping [Formula: see text] to itself form a group [Formula: see text], and the additive Hamming isometries form a larger group [Formula: see text]: [Formula: see text]. The main result says that these two subgroups can be as different as possible: for any two subgroups [Formula: see text], subject to some natural necessary conditions, there exists an additive code [Formula: see text] such that [Formula: see text] and [Formula: see text].

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39

DATTA, MAHUYA. "PARTIAL ISOMETRIES OF A SUB-RIEMANNIAN MANIFOLD." International Journal of Mathematics 23, no. 02 (February 2012): 1250043. http://dx.doi.org/10.1142/s0129167x12500437.

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In this article, we obtain the following generalization of isometric C1-immersion theorem of Nash and Kuiper. Let M be a smooth manifold of dimension m and H a rank k subbundle of the tangent bundle TM with a Riemannian metric gH. Then the pair (H, gH) defines a sub-Riemannian structure on M. We call a C1-map f : (M, H, gH) → (N, h) into a Riemannian manifold (N, h) a partial isometry if the derivative map df restricted to H is isometric, that is if f*h|H = gH. We prove that if f0 : M → N is a smooth map such that df0|H is a bundle monomorphism and [Formula: see text], then f0 can be homotoped to a C1-map f : M → N which is a partial isometry, provided dim N > k. As a consequence of this result, we obtain that every sub-Riemannian manifold (M, H, gH) admits a partial isometry in ℝn, provided n ≥ m + k.

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40

Jiménez-Vargas, A., and Moisés Villegas-Vallecillos. "2-Local Isometries on Spaces of Lipschitz Functions." Canadian Mathematical Bulletin 54, no. 4 (December 1, 2011): 680–92. http://dx.doi.org/10.4153/cmb-2011-025-5.

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AbstractLet (X, d) be a metric space, and let Lip(X) denote the Banach space of all scalar-valued bounded Lipschitz functions ƒ on X endowed with one of the natural normswhere L(ƒ) is the Lipschitz constant of ƒ. It is said that the isometry group of Lip(X) is canonical if every surjective linear isometry of Lip(X) is induced by a surjective isometry of X. In this paper we prove that if X is bounded separable and the isometry group of Lip(X) is canonical, then every 2-local isometry of Lip(X) is a surjective linear isometry. Furthermore, we give a complete description of all 2-local isometries of Lip(X) when X is bounded.

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41

Randrianantoanina, Beata. "Isometries of Hilbert space valued function spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 61, no. 2 (October 1996): 150–61. http://dx.doi.org/10.1017/s1446788700000161.

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AbstractLet X be a (real or complex) rearrangement-invariant function space on Ω (where Ω = [0, 1] or Ω ⊆ N) whose norm is not proportional to the L2-norm. Let H be a separable Hilbert space. We characterize surjective isometries of X (H). We prove that if T is such an isometry then there exist Borel maps a: Ω → + K and σ: Ω → Ω and a strongly measurable operator map S of Ω into B (H) so that for almost all ω, S(ω) is a surjective isometry of H, and for any f ∈ X(H), T f(ω) = a(ω)S(ω)(f(σ(ω))) a.e. As a consequence we obtain a new proof of the characterization of surjective isometries in complex rearrangement-invariant function spaces.

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42

Isangulova, D. V. "Sharp estimates of the geometric rigidity on the first Heisenberg group." Доклады Академии наук 488, no. 6 (October 30, 2019): 590–94. http://dx.doi.org/10.31857/s0869-56524886590-594.

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We prove quantitative stability of isometries on the first Heisenberg group with sub-Riemannian geometry: every (1 + )-quasi-isometry of the John domain of the Heisenberg group is close to some isometry with order of closeness in the uniform norm and with the order of closeness+ in the Sobolev norm. An example demonstrating the asymptotic sharpness of the results is given.

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43

Gherairi, Khadija, Zayd Hajjej, Haiyan Li, and Hedi Regeiba. "Some properties of $ n $-quasi-$ (m, q) $-isometric operators on a Banach space." AIMS Mathematics 8, no. 12 (2023): 31246–57. http://dx.doi.org/10.3934/math.20231599.

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<abstract><p>In this paper, we introduced the class of $ n $-quasi-$ (m, q) $-isometric operators on a Banach space. Such a class seems to be a natural generalization of $ m $-isometric operators on Banach spaces and of $ n $-quasi-$ m $-isometric operators on Hilbert spaces. We started by giving some of their elementary properties and studying the products and the power of such operators. Next, we focused on the dynamic of a $ n $-quasi-$ m $-isometry. More precisely, we proved a result by characterizing the supercyclicity of such a class.</p></abstract>

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44

Jasem, Milan. "On weak isometries in directed groups." Mathematica Slovaca 69, no. 5 (October 25, 2019): 989–98. http://dx.doi.org/10.1515/ms-2017-0283.

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Abstract In the paper weak isometries in directed groups are investigated. It is proved that for every weak isometry f in a directed group G the relation f(UL(x, y) ∩ LU(x, y)) = UL(f(x), f(y)) ∩ LU(f(x), f(y)) is valid for each x, y ∈ G. The notions of an orthogonality of two elements and of a subgroup symmetry in directed groups are introduced and it is shown that each weak isometry in a 2-isolated directed group or in an abelian directed group is a composition of a subgroup symmetry and a right translation. It is also proved that stable weak isometries in a 2-isolated abelian directed group G are directly related to subdirect decompositions of the subgroup G2 = {2x; x ∈ G} of G.

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45

Attele, K. R. M., and A. R. Lubin. "Models for joint isometries." Glasgow Mathematical Journal 38, no. 2 (May 1996): 191–94. http://dx.doi.org/10.1017/s0017089500031426.

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An N-tuple ℐ= (T1…, TN) of commuting contractions on a Hilbert space H is said to be a joint isometry if for all x in H, or, equivalently, if Athavale in [1] characterized the joint isometries as subnormal N-tuples whose minimal normal extensions have joint spectra in the unit sphere S2N−X a geometric perspective of this is given in [4]. Subsequently, V. Müller and F.-H. Vasilescu proved that commuting N-tuples which are joint contractions, i.e. , can be represented as restrictions of certain weighted shifts direct sum a joint isometry. In this paper we adapt the canonical models of [3], and also construct a new canonical model, which completes the previous descriptions by showing joint isometries are indeed restrictions of specific multivariable weighted shifts [2].

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46

Yang, Wenmao. "On O. Bonnet III-isometry of surfaces in three dimensional Euclidean space." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 49, no. 1 (August 1990): 90–110. http://dx.doi.org/10.1017/s1446788700030263.

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AbstractIn this paper we consider O. Bonnet III-isometry (or BIII-isometry) of surfaces in 3-dimensional Euclidean space E3 Suppose a map F: M → M* is a diffeomorphism, and F* (III*) = III, ki(m) = k*i (m*), i = 1, 2, where m ∈ M, m* ∈ M*, m* = F (m), ki and k*i are the principal curvatures of surfaces M and M* at the points m and m*, respectively, III and III* are the third fundmental forms of M and M*, respectively. In this case, we call F an O. Bonnet III-isometry from M to M*. O. Bonnet I-isometries were considered in references [1]-[5].We distinguish three cases about BIII-surfaces, which admits a non-trivial BIII-ismetry. We obtain some geometric properties of BIII-surfaces and BIII-isometries in these three cases; see Theorems 1, 2, 3 (in Section 2). We study some special BIII-surfaces: the minimal BIII-surfaces; BIII-surfaces of revolution; and BIII-surfaces with constant Gaussian curvature; see Theorems 4, 5, 6 (in Section 3).

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47

Oymak, Samet, Benjamin Recht, and Mahdi Soltanolkotabi. "Isometric sketching of any set via the Restricted Isometry Property." Information and Inference: A Journal of the IMA 7, no. 4 (March 7, 2018): 707–26. http://dx.doi.org/10.1093/imaiai/iax019.

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Abstract In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be computed in log-linear time, providing efficient dimensionality reduction of general sets. In particular, we show that using such matrices any set from high dimensions can be embedded into lower dimensions with near optimal distortion. We obtain our results by connecting dimensionality reduction of any set to dimensionality reduction of sparse vectors via a chaining argument.

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48

Martínez-García, Darío, Ángela Rodríguez-Perea, Álvaro Huerta-Ojeda, Daniel Jerez-Mayorga, Daniel Aguilar-Martínez, Ignacio Chirosa-Rios, Pablo Ruiz-Fuentes, and Luis Javier Chirosa-Rios. "Effects of Pre-Activation with Variable Intra-Repetition Resistance on Throwing Velocity in Female Handball Players: A Methodological Proposal." Journal of Human Kinetics 77, no. 1 (January 30, 2021): 235–44. http://dx.doi.org/10.2478/hukin-2021-0022.

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Abstract The purpose of this study was to investigate the acute effect of pre-activation with Variable Intra-Repetition Resistance and isometry on the overhead throwing velocity in handball players. Fourteen female handball players took part in the study (age: 21.2 ± 2.7 years, experience: 10.9 ± 3.5 years). For Post-Activation Potentiation, two pre-activation methods were used: (I) Variable Intra-Repetition Resistance: 1 x 5 maximum repetitions at an initial velocity of 0.6 m·s-1 and a final velocity of 0.9 m·s-1; (II) Isometry: 1 x 5 s of maximum voluntary isometric contraction. Both methods were "standing unilateral bench presses" with the dominant arm, using a functional electromechanical dynamometer. The variable analysed was the mean of the three overhead throws. Ball velocity was measured with a radar (Stalker ATS). The statistical analysis was performed using ANOVA with repeated measures. No significant differences were found for either method (variable resistance intra-repetition: p = 0.194, isometry: p = 0.596). Regarding the individual responses, the analysis showed that 86% of the sample increased throwing velocity with the variable resistance intra-repetition method, while 93% of the sample increased throwing velocity with the isometric method. Both the variable intra-repetition resistance and isometric methods show improvements in ball velocity in female handball players. However, the authors recommend checking individual responses, since the results obtained were influenced by the short rest interval between the pre-activation and the experimental sets.

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Maisyaroh, Arista, Devi Aulia Putri, Achlish Abdillah, and Eko Prasetya Widianto. "THE EFFECT OF ISOMETRIC EXERCISE ON BLOOD PRESSURE REDUCTION IN HYPERTENSION: A LITERATURE REVIEW." Nurse and Health: Jurnal Keperawatan 10, no. 2 (December 17, 2021): 162–74. http://dx.doi.org/10.36720/nhjk.v10i2.207.

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Background: Hypertension is a major factor contributing to cardiovascular disease, which is the number one cause of death globally. Basic Health Research Indonesian Ministry of Health data for 2018 showed that hypertension in East Java Province increased in 2018 by 36.32. So, the authors want to know the effect of isometrics on reducing blood pressure. Objective: The authors want to know the effect of isometrics on reducing blood pressure. Design: This study design is a systematic review to search and review article from database and the theory underlying this study or guidance in this systematic literature review using PRISMA. Data Sources: Based on the results of the literature search through six databases, such as EBSCO, Springer, MedPub, Elsevier, Science Direct, and National Nursing Journal with keywords: Hypertension, High Blood Pressure, Resting Blood Pressure, Isometric Training, Isometric Exercise. The data was search since June 2020. Review Methods: The method used in the preparation of the Literature review using the PRISMA checklist and PICOS. Secondary data obtained from the journal with a predetermined discussion. Results: Based on 18 articles in the literature review, it can be concluded that the results for the research is Isometric exercises that are performed are very effective in reducing blood pressure. Conclusion: Isometric exercises that are performed are very effective in reducing blood pressure. The exercise is doing in 3-4 weeks with 4x2 minutes of exercise with a rest duration of 3 minutes.

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50

Jeevanjee, Theresa L. "Isometries of Orbifolds Double-Covered by Lens Spaces." Journal of Knot Theory and Its Ramifications 12, no. 06 (September 2003): 819–32. http://dx.doi.org/10.1142/s0218216503002809.

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Let K be a two-bridge knot in S3. Then K is also denoted as the four-plat, b(p,q) to indicate its association with some rational number p/q. The lens space L = L(p,q) admits an isometry, τ, of order 2, such that the quotient space L modulo the involution τ is an orbifold whose exceptional set is K. In this paper, the isometries of these orbifolds are classified; this is equivalent to computing the isometries of (S3,K).

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