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Artykuły w czasopismach na temat „Hilbert space operators”

Autor: Grafiati

Data publikacji: 6 września 2023

Data aktualizacji: 31 lipca 2025

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1

Agniel, Vidal. "Unitary skew-dilations of Hilbert space operators." Extracta Mathematicae 35, no. 2 (2020): 137–84. http://dx.doi.org/10.17398/2605-5686.35.2.137.

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2

Kérchy, László. "Pluquasisimilar Hilbert space operators." Acta Scientiarum Mathematicarum 86, no. 34 (2020): 503–20. http://dx.doi.org/10.14232/actasm-020-973-4.

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3

Rugiri, Peter Githara. "Spectrum of bounded operators in Hilbert spaces." Editon Consortium Journal of Physical and Applied Sciences 3, no. 1 (2023): 102–8. http://dx.doi.org/10.51317/ecjpas.v3i1.411.

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This paper sought to study the spectrum operators by emphasising on condition of commuting operators so as to expose classes of operators. Here study of various classes of bounded operators on a Hilbert space H is one of the most important topics in the preparation of the study of the Hilbert spaces. In case a abounded operator A commutes at least with its own adjoint A* it forms important classes of operators on H, eg normal, unitary, self – adjoint etc. The operators under the study are bounded operators operating in a complete space called Hilbert spaces.

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4

Dixmier, Jacques. "Operateurs hypofermes." Journal of Operator Theory 91, no. 2 (2024): 323–33. https://doi.org/10.7900/jot.2023nov13.2451.

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Range spaces of bounded linear operators between Hilbert spaces, as well as linear operators between Hilbert spaces, whose graph is a bounded linear range of some Hilbert space, were systematically studied in an early paper. Here extensions of the above topics to the framework of general Banach spaces are discussed. A hypoclosed linear subspace of a Banach space is the range space of a bounded linear operator defined on some Banach space, while a hypoclosed linear operator is a linear operator between Banach spaces, whose graph is hypoclosed. Characterizations, permanence properties, pathologi

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5

Carmo, Joao R., and S. Waleed Noor. "Universal composition operators." Journal of Operator Theory 87, no. 1 (2021): 137–56. http://dx.doi.org/10.7900/jot.2020aug03.2301.

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A Hilbert space operator U is called \textit{universal} (in the sense of Rota) if every Hilbert space operator is similar to a multiple of U restricted to one of its invariant subspaces. It follows that the \textit{invariant subspace problem} for Hilbert spaces is equivalent to the statement that all minimal invariant subspaces for U are one dimensional. In this article we characterize all linear fractional composition operators Cϕf=f∘ϕ that have universal translates on both the classical Hardy spaces H2(C+) and H2(D) of the half-plane and the unit disk, respectively. The new example here is t

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6

Jarchow, Hans. "Factoring absolutely summing operators through Hilbert-Schmidt operators." Glasgow Mathematical Journal 31, no. 2 (1989): 131–35. http://dx.doi.org/10.1017/s0017089500007643.

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Let K be a compact Hausdorff space, and let C(K) be the corresponding Banach space of continuous functions on K. It is well-known that every 1-summing operator S:C(K)→l2 is also nuclear, and therefore factors S = S1S2, with S1:l2→l2 a Hilbert–Schmidt operator and S1:C(K)→l2 a bounded operator. It is easily seen that this latter property is preserved when C(K) is replaced by any quotient, and that a Banach space X enjoys this property if and only if its second dual, X**, does. This led A. Pełczyński [15] to ask if the second dual of a Banach space X must be isomorphic to a quotient of a C(K)-sp

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7

Krnić, Mario. "Hilbert-type inequalities for Hilbert space operators." Quaestiones Mathematicae 36, no. 2 (2013): 209–23. http://dx.doi.org/10.2989/16073606.2013.801148.

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8

JUNG, IL BONG, EUNGIL KO, and CARL PEARCY. "ALMOST INVARIANT HALF-SPACES FOR OPERATORS ON HILBERT SPACE." Bulletin of the Australian Mathematical Society 97, no. 1 (2017): 133–40. http://dx.doi.org/10.1017/s0004972717000533.

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The theory of almost invariant half-spaces for operators on Banach spaces was begun recently and is now under active development. Much less attention has been given to almost invariant half-spaces for operators on Hilbert space, where some techniques and results are available that are not present in the more general context of Banach spaces. In this note, we begin such a study. Our much simpler and shorter proofs of the main theorems have important consequences for the matricial structure of arbitrary operators on Hilbert space.

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9

Moghaddam, Sadaf Fakri, та Alireza Kamel Mirmostafaee. "Numerical Radius of Bounded Operators with ℓ ^p -Norm". Tatra Mountains Mathematical Publications 81, № 1 (2022): 155–64. http://dx.doi.org/10.2478/tmmp-2022-0012.

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Abstract We study the numerical radius of bounded operators on direct sum of a family of Hilbert spaces with respect to the ℓ p -norm, where 1 ≤ p ≤∞. We propose a new method which enables us to prove validity of many inequalities on numerical radius of bounded operators on Hilbert spaces when the underling space is a direct sum of Hilbert spaces with ℓ p -norm, where 1 ≤ p ≤ 2. We also provide an example to show that some known results on numerical radius are not true for a space that is the set of bounded operators on ℓ p -sum of Hilbert spaces where 2 <p < ∞. We also present some appl

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10

MacLennan, Bruce James. "Cognition in Hilbert space." Behavioral and Brain Sciences 36, no. 3 (2013): 296–97. http://dx.doi.org/10.1017/s0140525x1200283x.

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AbstractUse of quantum probability as a top-down model of cognition will be enhanced by consideration of the underlying complex-valued wave function, which allows a better account of interference effects and of the structure of learned and ad hoc question operators. Furthermore, the treatment of incompatible questions can be made more quantitative by analyzing them as non-commutative operators.

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11

Vaccaro, John A. "Phase operators on Hilbert space." Physical Review A 51, no. 4 (1995): 3309–17. http://dx.doi.org/10.1103/physreva.51.3309.

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12

Leung, Denny H. "Factoring operators through Hilbert space." Israel Journal of Mathematics 71, no. 2 (1990): 225–27. http://dx.doi.org/10.1007/bf02811886.

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13

Boenkost, W., and F. Constantinescu. "Vertex operators in Hilbert space." Journal of Mathematical Physics 34, no. 8 (1993): 3607–15. http://dx.doi.org/10.1063/1.530048.

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14

Khrushchev, Sergei, and Vladimir Peller. "Hankel operators on Hilbert space." Acta Applicandae Mathematicae 5, no. 1 (1986): 96–100. http://dx.doi.org/10.1007/bf00049173.

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15

Bhardwaj, Ruchi, S. K. Sharma, and S. K. Kaushik. "Trace class operators via OPV-frames." Filomat 35, no. 13 (2021): 4353–68. http://dx.doi.org/10.2298/fil2113353b.

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Trace class operators for quaternionic Hilbert spaces (QHS) were studied by Moretti and Oppio [18]. In this paper, we study trace class operators via operator valued frames (OPV-frames). We introduce OPV-frames in a right quaternionic Hilbert space H with range in a two sided quaternionic Hilbert space K and obtain various results including several characterizations of OPV-frames. Also, we obtain a necessary and sufficient condition for a bounded operator on a right QHS to be a trace class operator which generalizes a similar result by Attal [2]. Moreover, we construct a trace class operator o

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16

kian, Mohsen. "Hardy--Hilbert type inequalities for Hilbert space operators." Annals of Functional Analysis 3, no. 2 (2012): 128–34. http://dx.doi.org/10.15352/afa/1399899937.

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17

Burtnyak, I., I. Chernega, V. Hladkyi, O. Labachuk, and Z. Novosad. "Application of symmetric analytic functions to spectra of linear operators." Carpathian Mathematical Publications 13, no. 3 (2021): 701–10. http://dx.doi.org/10.15330/cmp.13.3.701-710.

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The paper is devoted to extension of the theory of symmetric analytic functions on Banach sequence spaces to the spaces of nuclear and $p$-nuclear operators on the Hilbert space. We introduced algebras of symmetric polynomials and analytic functions on spaces of $p$-nuclear operators, described algebraic bases of such algebras and found some connection with the Fredholm determinant of a nuclear operator. In addition, we considered cases of compact and bounded normal operators on the Hilbert space and discussed structures of symmetric polynomials on corresponding spaces.

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18

Novosad, Z. H. "Topological transitivity of translation operators in a non-separable Hilbert space." Carpathian Mathematical Publications 15, no. 1 (2023): 278–85. http://dx.doi.org/10.15330/cmp.15.1.278-285.

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We consider a Hilbert space of entire analytic functions on a non-separable Hilbert space, associated with a non-separable Fock space. We show that under some conditions operators, like the differentiation operators and translation operators, are topologically transitive in this space.

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19

Alshammari, Hadi Obaid. "Extension of m-Symmetric Hilbert Space Operators." Journal of Mathematics 2022 (December 28, 2022): 1–8. http://dx.doi.org/10.1155/2022/5272632.

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We introduce a new class of operators, which we will call the class of P -quasi- m -symmetric operators that includes m -symmetric operators and k -quasi m -symmetric operators. Some basic structural properties of this class of operators are established based on the operator matrix representation associated with such operators.

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20

Roopaei, Hadi. "Bounds of operators on the Hilbert sequence space." Concrete Operators 7, no. 1 (2020): 155–65. http://dx.doi.org/10.1515/conop-2020-0104.

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AbstractThe author has computed the bounds of the Hilbert operator on some sequence spaces [18, 19]. Through this study the author has investigated the bounds of operators on the Hilbert sequence space and the present study is a complement of those previous research.

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21

Hedayatian, Karim, and Mohammad Namegoshayfard. "Commutant hypercyclicity of Hilbert space operators." Filomat 37, no. 15 (2023): 4857–68. http://dx.doi.org/10.2298/fil2315857h.

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An operator T on a Hilbert space H is commutant hypercyclic if there is a vector x in H such that the set {Sx : TS = ST} is dense in H. We prove that operators on finite dimensional Hilbert space, a rich class of weighted shift operators, isometries, exponentially isometries and idempotents are all commutant hypercyclic. Then we discuss on commutant hypercyclicity of 2 ? 2 operator matrices. Moreover, for each integer number n ? 2, we give a commutant hypercyclic nilpotent operator of order n on an infinite dimensional Hilbert space. Finally, we study commutant transitivity of operators and gi

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22

Babenko, V. F., N. V. Parfinovych, and D. S. Skorokhodov. "The best approximation of closed operators by bounded operators in Hilbert spaces." Carpathian Mathematical Publications 14, no. 2 (2022): 453–63. http://dx.doi.org/10.15330/cmp.14.2.453-463.

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We solve the problem of the best approximation of closed operators by linear bounded operators in Hilbert spaces under assumption that the operator transforms orthogonal basis in Hilbert space into an orthogonal system. As a consequence, sharp additive Hardy-Littlewood-Pólya type inequality for multiple closed operators is established. We also demonstrate application of these results in concrete situations: for the best approximation of powers of the Laplace-Beltrami operator on classes of functions defined on closed Riemannian manifolds, for the best approximation of differentiation operators

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23

Amson, J. C., and N. Gopal Reddy. "A Hilbert algebra of Hilbert-Schmidt quadratic operators." Bulletin of the Australian Mathematical Society 41, no. 1 (1990): 123–34. http://dx.doi.org/10.1017/s0004972700017913.

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A quadratic operator Q of Hilbert-Schmidt class on a real separable Hilbert space H is shown to be uniquely representable as a sequence of self-adjoint linear operators of Hilbert-Schmidt class on H, such that Q(x) = Σk〈Lkx, x〉uk with respect to a Hilbert basis . It is shown that with the norm | ‖Q‖ | = (Σk ‖Lk‖2)½ and inner-product 〈〈〈Q, P〉〉〉 = Σk 〈〈Lk, Mk〉〉, together with a multiplication defined componentwise through the composition of the linear components, the vector space of all Hilbert-Schmidt quadratic operators Q on H becomes a linear H*-algebra containing an ideal of nuclear (trace c

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24

Cabrera, M., J. Martínez, and A. Rodríguez. "Hilbert modules revisited: orthonormal bases and Hilbert-Schmidt operators." Glasgow Mathematical Journal 37, no. 1 (1995): 45–54. http://dx.doi.org/10.1017/s0017089500030378.

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The concept of a Hilbert module (over an H*-algebra) arises as a generalization of that of a complex Hilbert space when the complex field is replaced by an (associative) H*-algebra with zero annihilator. P. P. Saworotnow [13] introduced Hilbert modules and extended to its context some classical theorems from the theory of Hilbert spaces, J. F. Smith [17] gave a complete structure theory for Hilbert modules, and G. R. Giellis [9] obtained a nice characteristization of Hilbert modules.

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25

Bercovici, Hari. "Three Test Problems for Quasisimilarity." Canadian Journal of Mathematics 39, no. 4 (1987): 880–92. http://dx.doi.org/10.4153/cjm-1987-043-x.

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Kaplansky proposed in [7] three problems with which to test the adequacy of a proposed structure theory of infinite abelian groups. These problems can be rephrased as test problems for a structure theory of operators on Hilbert space. Thus, R. Kadison and I. Singer answered in [6] these test problems for the unitary equivalence of operators. We propose here a study of these problems for quasisimilarity of operators on Hilbert space. We recall first that two (bounded, linear) operators T and T′ acting on the Hilbert spaces and , are said to be quasisimilar if there exist bounded operators and w

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26

Holub, J. R. "On Shift Operators." Canadian Mathematical Bulletin 31, no. 1 (1988): 85–94. http://dx.doi.org/10.4153/cmb-1988-013-8.

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AbstractA definition of an isometric shift operator on a Banach space is given which extends the usual definition of a shift operator on a separable Hilbert space. It is shown that there is no such shift on many of the common Banach spaces of continuous functions. The associated ideas of a semi-shift and a backward shift are also introduced and studied in the case of continuous function spaces.

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27

Ploymukda, Arnon, and Pattrawut Chansangiam. "Norm estimations, continuity, and compactness for Khatri-Rao products of Hilbert Space operators." Malaysian Journal of Fundamental and Applied Sciences 14, no. 4 (2018): 382–86. http://dx.doi.org/10.11113/mjfas.v14n4.881.

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We provide estimations for the operator norm, the trace norm, and the Hilbert-Schmidt norm for Khatri-Rao products of Hilbert space operators. It follows that the Khatri-Rao product is continuous on norm ideals of compact operators equipped with the topologies induced by such norms. Moreover, if two operators are represented by block matrices in which each block is nonzero, then their Khatri-Rao product is compact if and only if both operators are compact. The Khatri-Rao product of two operators are trace-class (Hilbert-Schmidt class) if and only if each factor is trace-class (Hilbert-Schmidt

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28

TRAPANI, C. "QUASI *-ALGEBRAS OF OPERATORS AND THEIR APPLICATIONS." Reviews in Mathematical Physics 07, no. 08 (1995): 1303–32. http://dx.doi.org/10.1142/s0129055x95000475.

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The main facts of the theory of quasi*-algebras of operators acting in a rigged Hilbert space are reviewed. The particular case where the rigged Hilbert space is generated by a self-adjoint operator in Hilbert space is examined in more details. A series of applications to quantum theories are discussed.

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29

Minculete, Nicuşor. "About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators." Symmetry 13, no. 2 (2021): 305. http://dx.doi.org/10.3390/sym13020305.

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The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear operators on a Hilbert space, where we mention Bohr’s inequality and Bergström’s inequality for operators. We present an inequality of the Cauchy–Bunyakovsky–Schwarz type for bounded linear operators, by the technique of the monotony of a sequence. We also prove a refinement of the Aczél inequality for b

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30

Celeghini, Enrico, Manuel Gadella, and Mariano A. del Olmo. "Groups, Special Functions and Rigged Hilbert Spaces." Axioms 8, no. 3 (2019): 89. http://dx.doi.org/10.3390/axioms8030089.

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We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions serve as bases for infinite dimensional Hilbert spaces supporting linear unitary irreducible representations of a given Lie group. These representations are explicitly given by operators on the Hilbert space H and the generators of the Lie algebra are represented by unbounded self-adjoint operators. The action of these operators on elements of contin

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31

Edith, Warue, Sammy W. Musundi, and Jeremiah K. Ndung’u. "On Some Properties of Square Normal Operators." Journal of Advances in Mathematics and Computer Science 39, no. 8 (2024): 68–78. http://dx.doi.org/10.9734/jamcs/2024/v39i81922.

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The study of operators in Hilbert spaces is an important concept due to its wide application in areas like computer programming, financial mathematics and quantum physics. This paper focused on a class of square normal operators in a Hilbert space. Let H be a complex Hilbert space and B(H) be a bounded linear operator acting on H. Then an operator T in B(H) is a square normal if T2(T*)2 = (T*)2T2. This paper studied the commutation relations and properties of this class of operators and showed that for any square normal operator T, then T* and T-1 if it exists is square normal. Furthermore, th

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32

Evans, Mogoi. "Orthogonal Polynomials and Operator Convergence in Hilbert Spaces: Norm-Attainability, Uniform Boundedness, and Compactness." Asian Research Journal of Mathematics 19, no. 10 (2023): 227–34. http://dx.doi.org/10.9734/arjom/2023/v19i10744.

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This research paper investigates the convergence properties of operators constructed from orthogonal polynomials in the context of Hilbert spaces. The study establishes norm-attainability and explores the uniform boundedness of these operators, extending the analysis to include complex-valued orthogonal polynomials. Additionally, the paper uncovers connections between operator compactness and the convergence behaviors of orthogonal polynomial operators, revealing how sequences of these operators converge weakly to both identity and zero operators. These results advance our understanding of the

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33

Wong, M. W. "Minimal and Maximal Operator Theory With Applications." Canadian Journal of Mathematics 43, no. 3 (1991): 617–27. http://dx.doi.org/10.4153/cjm-1991-036-7.

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AbstractLetXbe a complex Banach space andAa linear operator fromXintoXwith dense domain. We construct the minimal and maximal operators of the operatorAand prove that they are equal under reasonable hypotheses on the spaceXand operatorA. As an application, we obtain the existence and regularity of weak solutions of linear equations on the spaceX. As another application we obtain a criterion for a symmetric operator on a complex Hilbert space to be essentially self-adjoint. An application to pseudo-differential operators of the Weyl type is given.

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34

KällstrÖm, A., and B. D. Sleeman. "Joint spectra for commuting operators." Proceedings of the Edinburgh Mathematical Society 28, no. 2 (1985): 233–48. http://dx.doi.org/10.1017/s0013091500022677.

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The theory of joint spectra for commuting operators in a Hilbert space has recently been studied by several authors (Vasilescu [11,12], Curto [4,5], and Cho-Takaguchi[2,3]). In this paper we willuse the definition by Taylor [10] of the joint spectrum to show that thejoint spectrum is determined by the action of certain "Laplacians"(cf. Curto [4,5]) of a chain-complex of Hilbert spaces.

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35

Altwaijry, Najla, Kais Feki, and Shigeru Furuichi. "Generalized Cauchy–Schwarz Inequalities and A-Numerical Radius Applications." Axioms 12, no. 7 (2023): 712. http://dx.doi.org/10.3390/axioms12070712.

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The purpose of this research paper is to introduce new Cauchy–Schwarz inequalities that are valid in semi-Hilbert spaces, which are generalizations of Hilbert spaces. We demonstrate how these new inequalities can be employed to derive novel A-numerical radius inequalities, where A denotes a positive semidefinite operator in a complex Hilbert space. Some of our novel A-numerical radius inequalities expand upon the existing literature on numerical radius inequalities with Hilbert space operators, which are important tools in functional analysis. We use techniques from semi-Hilbert space theory t

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36

Abderramán Marrero, J., and V. Tomeo. "Arrowhead operators on a Hilbert space." Operators and Matrices, no. 3 (2016): 593–609. http://dx.doi.org/10.7153/oam-10-34.

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37

Kérchy, László. "Unitary asymptotes of Hilbert space operators." Banach Center Publications 30, no. 1 (1994): 191–201. http://dx.doi.org/10.4064/-30-1-191-201.

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38

Cegielski, Andrzej, and Yair Censor. "On Componental Operators in Hilbert Space." Numerical Functional Analysis and Optimization 42, no. 13 (2021): 1555–71. http://dx.doi.org/10.1080/01630563.2021.2006695.

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39

Yakubovich, Dmitry, and Sameer Chavan. "Spherical tuples of Hilbert space operators." Indiana University Mathematics Journal 64, no. 2 (2015): 577–612. http://dx.doi.org/10.1512/iumj.2015.64.5471.

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40

Morassaei, A., F. Mirzapour, and M. S. Moslehian. "Bellman inequality for Hilbert space operators." Linear Algebra and its Applications 438, no. 10 (2013): 3776–80. http://dx.doi.org/10.1016/j.laa.2011.06.042.

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41

Hirzallah, Omar. "Commutator inequalities for Hilbert space operators." Linear Algebra and its Applications 431, no. 9 (2009): 1571–78. http://dx.doi.org/10.1016/j.laa.2009.05.026.

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42

Khatskevich, V. A., M. I. Ostrovskii, and V. S. Shulman. "Quadratic Inequalities for Hilbert Space Operators." Integral Equations and Operator Theory 59, no. 1 (2007): 19–34. http://dx.doi.org/10.1007/s00020-007-1511-3.

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43

Prǎjiturǎ, Gabriel T. "Irregular vectors of Hilbert space operators." Journal of Mathematical Analysis and Applications 354, no. 2 (2009): 689–97. http://dx.doi.org/10.1016/j.jmaa.2009.01.034.

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44

Glasser, M. L. "Exponentials of Certain Hilbert Space Operators." SIAM Review 33, no. 3 (1991): 472. http://dx.doi.org/10.1137/1033103.

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45

ć Hot, Jadranka Mić, Josip Pečarić, and Marjan Praljak. "Levinson's inequality for Hilbert space operators." Journal of Mathematical Inequalities, no. 4 (2015): 1271–85. http://dx.doi.org/10.7153/jmi-09-97.

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46

Drivaliaris, Dimosthenis, and Nikos Yannakakis. "Hilbert space structure and positive operators." Journal of Mathematical Analysis and Applications 305, no. 2 (2005): 560–65. http://dx.doi.org/10.1016/j.jmaa.2004.12.007.

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47

Cheung, Wing-Sum, and Josip Pečarić. "Bohr's inequalities for Hilbert space operators." Journal of Mathematical Analysis and Applications 323, no. 1 (2006): 403–12. http://dx.doi.org/10.1016/j.jmaa.2005.10.046.

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48

Sababheh, Mohammad, and Hamid Reza Moradi. "New orders among Hilbert space operators." Mathematical Inequalities & Applications, no. 2 (2023): 415–32. http://dx.doi.org/10.7153/mia-2023-26-27.

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McDonald, G., and C. Sundberg. "On the Spectra of Unbounded Subnormal Operators." Canadian Journal of Mathematics 38, no. 5 (1986): 1135–48. http://dx.doi.org/10.4153/cjm-1986-057-x.

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Putnam showed in [5] that the spectrum of the real part of a bounded subnormal operator on a Hilbert space is precisely the projection of the spectrum of the operator onto the real line. (In fact he proved this more generally for bounded hyponormal operators.) We will show that this result can be extended to the class of unbounded subnormal operators with bounded real parts.Before proceeding we establish some notation. If T is a (not necessarily bounded) operator on a Hilbert space, then D(T) will denote its domain, and σ(T) its spectrum. For K a subspace of D(T), T|K will denote the restricti

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Guesba, Messaoud, Pintu Bhunia, and Kallol Paul. "A-numerical radius inequalities and A-translatable radii of semi-Hilbert space operators." Filomat 37, no. 11 (2023): 3443–56. https://doi.org/10.2298/fil2311443g.

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We develop A-numerical radius inequalities of the product and the commutator of semi-Hilbert space operators using the notion of A-numerical radius distance and A-seminorm distance. Further, we introduce a pair of translatable radii of semi-Hilbert space operators in the direction of another operator and obtain related inequalities which generalize the relevant inequalities studied in the setting of Hilbert space.

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