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Relevant bibliographies by topics / Operator theory – Linear spaces and algebras of operators – Operator spaces (= matricially normed spaces)

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Academic literature on the topic 'Operator theory – Linear spaces and algebras of operators – Operator spaces (= matricially normed spaces)'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Operator theory – Linear spaces and algebras of operators – Operator spaces (= matricially normed spaces)"

1

Bachir, A., and A. Segres. "Numerical range and orthogonality in normed spaces." Filomat 23, no. 1 (2009): 21–41. http://dx.doi.org/10.2298/fil0901021b.

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Introducing the concept of the normalized duality mapping on normed linear space and normed algebra, we extend the usual definitions of the numerical range from one operator to two operators. In this note we study the convexity of these types of numerical ranges in normed algebras and linear spaces. We establish some Birkhoff-James orthogonality results in terms of the algebra numerical range V (T)A which generalize those given by J.P. William and J.P. Stamplfli. Finally, we give a positive answer of the Mathieu's question. .

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2

Sharma, Mami, and Debajit Hazarika. "Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and its Fuzzy Compactness." New Mathematics and Natural Computation 16, no. 01 (March 2020): 177–93. http://dx.doi.org/10.1142/s1793005720500118.

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In this paper, we first investigate the relationship between various notions of fuzzy boundedness of linear operators in fuzzy normed linear spaces. We also discuss the fuzzy boundedness of fuzzy compact operators. Furthermore, the spaces of fuzzy compact operators have been studied.

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Cabral, Rodrigo A. H. M. "Strongly elliptic operators and exponentiation of operator Lie algebras." MATHEMATICA SCANDINAVICA 127, no. 2 (August 31, 2021): 264–86. http://dx.doi.org/10.7146/math.scand.a-126020.

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An intriguing feature which is often present in theorems regardingthe exponentiation of Lie algebras of unbounded linear operators onBanach spaces is the assumption of hypotheses on the Laplacianoperator associated with a basis of the operator Lie algebra.The main objective of this work is to show that one can substitutethe Laplacian by an arbitrary operator in the enveloping algebra andstill obtain exponentiation, as long as its closure generates astrongly continuous one-parameter semigroup satisfying certain normestimates, which are typical in the theory of strongly ellipticoperators.

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4

Frank, Michael. "Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules." Journal of K-theory 2, no. 3 (March 4, 2008): 453–62. http://dx.doi.org/10.1017/is008001031jkt035.

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AbstractC*-algebras A of compact operators are characterized as those C*-algebras of coefficients of Hilbert C*-modules for which (i) every bounded A-linear operator between two Hilbert A-modules possesses an adjoint operator, (ii) the kernels of all bounded A-linear operators between Hilbert A-modules are orthogonal summands, (iii) the images of all bounded A-linear operators with closed range between Hilbert A-modules are orthogonal summands, and (iv) for every Hilbert A-module every Hilbert A-submodule is a topological summand. Thus, the theory of Hilbert C*-modules over C*-algebras of compact operators has similarities with the theory of Hilbert spaces. In passing, we obtain a general closed graph theorem for bounded module operators on arbitrary Hilbert C*-modules.

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5

Burgin, Mark. "Fuzzy Continuity of Almost Linear Operators." International Journal of Fuzzy System Applications 3, no. 1 (January 2013): 40–50. http://dx.doi.org/10.4018/ijfsa.2013010103.

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In this paper, the author studies relations between fuzzy continuity and boundedness of approximately linear operators in the context of neoclassical analysis. The main result of this paper (Theorem 1) demonstrates that for approximately linear operators, fuzzy continuity is equivalent to boundedness when the continuity defect (or measure of discontinuity) is sufficiently small. The classical result that describes continuity of linear operators becomes a direct corollary of this theorem. Applying Theorem 1, we demonstrate (Theorem 2) that for linear operators in normed vector spaces, fuzzy continuity coincides with continuity when the continuity defect is sufficiently small, i.e., when it is less than one. Results are oriented at applications in physics, theory of information and other fields where operator equations play an important role. Several open problems and directions for future research are considered at the end of the paper.

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Iovino, José. "On the maximality of logics with approximations." Journal of Symbolic Logic 66, no. 4 (December 2001): 1909–18. http://dx.doi.org/10.2307/2694984.

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In this paper we analyze some aspects of the question of using methods from model theory to study structures of functional analysis.By a well known result of P. Lindström, one cannot extend the expressive power of first order logic and yet preserve its most outstanding model theoretic characteristics (e.g., compactness and the Löwenheim-Skolem theorem). However, one may consider extending the scope of first order in a different sense, specifically, by expanding the class of structures that are regarded as models (e.g., including Banach algebras or other structures of functional analysis), and ask whether the resulting extensions of first order model theory preserve some of its desirable characteristics.A formal framework for the study of structures based on Banach spaces from the perspective of model theory was first introduced by C. W. Henson in [8] and [6]. Notions of syntax and semantics for these structures were defined, and it was shown that using them one obtains a model theoretic apparatus that satisfies many of the fundamental properties of first order model theory. For instance, one has compactness, Löwenheim-Skolem, and omitting types theorems. Further aspects of the theory, namely, the fundamentals of stability and forking, were first introduced in [10] and [9].The classes of mathematical structures formally encompassed by this framework are normed linear spaces, possibly expanded with additional structure, e.g., operations, real-valued relations, and constants. This notion subsumes wide classes of structures from functional analysis. However, the restriction that the universe of a structure be a normed space is not necessary. (This restriction has a historical, rather than technical origin; specifically, the development of the theory was originally motivated by questions in Banach space geometry.) Analogous techniques can be applied if the universe is a metric space. Now, when the underlying metric topology is discrete, the resulting model theory coincides with first order model theory, so this logic extends first order in the sense described above. Furthermore, without any cost in the mathematical complexity, one can also work in multi-sorted contexts, so, for instance, one sort could be an operator algebra while another is. say, a metric space.

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7

Bauer, Wolfram, V. B. Kiran Kumar, and Rahul Rajan. "Korovkin-type theorems on $$B({\mathcal {H}})$$ and their applications to function spaces." Monatshefte für Mathematik, April 26, 2021. http://dx.doi.org/10.1007/s00605-021-01549-1.

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AbstractWe prove Korovkin-type theorems in the setting of infinite dimensional Hilbert space operators. The classical Korovkin theorem unified several approximation processes. Also, the non-commutative versions of the theorem were obtained in various settings such as Banach algebras, $$C^{*}$$ C ∗ -algebras and lattices etc. The Korovkin-type theorem in the context of preconditioning large linear systems with Toeplitz structure can be found in the recent literature. In this article, we obtain a Korovkin-type theorem on $$B({\mathcal {H}})$$ B ( H ) which generalizes all such results in the recent literature. As an application of this result, we obtain Korovkin-type approximation for Toeplitz operators acting on various function spaces including Bergman space $$A^{2}({\mathbb {D}})$$ A 2 ( D ) , Fock space $$F^{2}({\mathbb {C}})$$ F 2 ( C ) etc. These results are closely related to the preconditioning problem for operator equations with Toeplitz structure on the unit disk $${\mathbb {D}}$$ D and on the whole complex plane $${\mathbb {C}}$$ C . It is worthwhile to notice that so far such results are available for Toeplitz operators on circle only. This also establishes the role of Korovkin-type approximation techniques on function spaces with certain oscillation property. To address the function theoretic questions using these operator theory tools will be an interesting area of further research.

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8

Sheng, Yunhe, Jia Zhao, and Yanqiu Zhou. "Nijenhuis operators, product structures and complex structures on Lie–Yamaguti algebras." Journal of Algebra and Its Applications, July 24, 2020, 2150146. http://dx.doi.org/10.1142/s0219498821501462.

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In this paper, first, we study linear deformations of a Lie–Yamaguti algebra and introduce the notion of a Nijenhuis operator. Then we introduce the notion of a product structure on a Lie–Yamaguti algebra, which is a Nijenhuis operator [Formula: see text] satisfying [Formula: see text]. There is a product structure on a Lie–Yamaguti algebra if and only if the Lie–Yamaguti algebra is the direct sum of two subalgebras (as vector spaces). There are some special product structures, each of which corresponds to a special decomposition of the original Lie–Yamaguti algebra. In the same way, we introduce the notion of a complex structure on a Lie–Yamaguti algebra. Finally, we add a compatibility condition between a product structure and a complex structure to introduce the notion of a complex product structure on a Lie–Yamaguti algebra.

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Dissertations / Theses on the topic "Operator theory – Linear spaces and algebras of operators – Operator spaces (= matricially normed spaces)"

1

"Operators between ordered normed spaces." Chinese University of Hong Kong, 1991. http://library.cuhk.edu.hk/record=b5886856.

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by Chi-keung Ng.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1991.
Includes bibliographical references.
Introduction --- p.1
Chapter Chapter 0. --- Preliminary --- p.4
Chapter 0.1 --- Topological vector spaces
Chapter 0.2 --- Ordered vector spaces
Chapter 0.3 --- Ordered normed spaces
Chapter 0.4 --- Ordered topological vector spaces
Chapter 0.5 --- Ordered bornological vector spaces
Chapter Chapter 1. --- Results on Ordered Normed Spaces --- p.23
Chapter 1.1 --- Results on e∞-spaces and e1-spaces
Chapter 1.2 --- Complemented subspaces of ordered normed spaces
Chapter 1.3 --- Half injections and Half surjections
Chapter 1.4 --- Strict quotients and strict subspaces
Chapter Chapter 2. --- Helley's Selection Theorem and Local Reflexivity Theorem of order type --- p.55
Chapter 2.1 --- Helley's selection theorem of order type
Chapter 2.2 --- Local reflexivity theorem of order type
Chapter Chapter 3. --- Operator Modules and Ideal Cones --- p.68
Chapter 3.1 --- Operator modules and ideal cones
Chapter 3.2 --- Space cones and space modules
Chapter 3.3 --- Injectivity and surjectivity
Chapter 3. 4 --- Dual and pre-dual
Chapter Chapter 4. --- Topologies and Bornologies Defined by Operator Modules and Ideal Cones --- p.95
Chapter 4.1 --- Generalized polars
Chapter 4.2 --- Topologies and bornologies defined by β and ε
Chapter 4. 3 --- Injectivity and generating topologies
Chapter 4.4 --- Surjectivity and generating bornologies
Chapter 4.5 --- The solid property and the generating topologies
Chapter 4.6 --- The solid property and the generating bornologies
Chapter Chapter 5. --- Semi-norms and Bounded disks defined by Operator Modules and Ideal Cones --- p.129
Chapter 5.1 --- Results on semi-norms
Chapter 5.2 --- Results on bounded disks
References --- p.146
Notations --- p.149

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2

Thompson, Derek Allen. "Restrictions to Invariant Subspaces of Composition Operators on the Hardy Space of the Disk." 2014. http://hdl.handle.net/1805/3881.

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Indiana University-Purdue University Indianapolis (IUPUI)
Invariant subspaces are a natural topic in linear algebra and operator theory. In some rare cases, the restrictions of operators to different invariant subspaces are unitarily equivalent, such as certain restrictions of the unilateral shift on the Hardy space of the disk. A composition operator with symbol fixing 0 has a nested sequence of invariant subspaces, and if the symbol is linear fractional and extremally noncompact, the restrictions to these subspaces all have the same norm and spectrum. Despite this evidence, we will use semigroup techniques to show many cases where the restrictions are still not unitarily equivalent.

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Books on the topic "Operator theory – Linear spaces and algebras of operators – Operator spaces (= matricially normed spaces)"

1

(Victor), Vinnikov V., ed. Foundations of free noncommutative function theory. Providence, Rhode Island: American Mathematical Society, 2014.

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2

Simon, Barry. Operator theory. Providence, Rhode Island: American Mathematical Society, 2015.

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3

1959-, Blasco Oscar, and Universidad Politécnica de Valencia, eds. Topics in complex analysis and operator theory: Third Winter School Complex Analysis and Operator theory, February 2-5, 2010, Universidad Politécnica de Valencia, Valencia, Spain. Providence, R.I: American Mathematical Society, 2012.

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4

Krzysztof, Jarosz, ed. Function spaces in modern analysis: Sixth Conference on Function Spaces, May 18-22, 2010, Southern Illinois University, Edwardsville. Providence, R.I: American Mathematical Society, 2011.

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A, Kaashoek M., Lancaster Peter, Langer Heinz, Lerer Leonid, and SpringerLink (Online service), eds. A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial Volume. Basel: Springer Basel, 2012.

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Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View toward Coherent Sheaves (2006 Cambridge, Mass.). Grassmannians, moduli spaces, and vector bundles: Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View towards Coherent Sheaves, October 6-11, 2006, Cambridge, Massachusetts. Edited by Ellwood D. (David) 1966- and Previato Emma. Providence, RI: American Mathematical Society, 2011.

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7

Regularised integrals, sums, and traces: An analytic point of view. Providence, R.I: American Mathematical Society, 2012.

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Germany) International Conference on p-adic Functional Analysis (13th 2014 Paderborn. Advances in non-Archimedean analysis: 13th International Conference on p-adic Functional Analysis, August 12-16, 2014, University of Paderborn, Paderborn, Germany. Edited by Glöckner Helge 1969 editor, Escassut Alain editor, and Shamseddine Khodr 1966 editor. Providence, Rhode Island: American Mathematical Society, 2016.

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Advances In Ultrametric Analysis 12th International Conference On Padic Functional Analysis July 26 2012 University Of Manitoba Winnipeg Canada. American Mathematical Society, 2013.

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