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Journal articles on the topic 'Bounded linear operator'

Author: Grafiati

Published: 10 December 2022

Last updated: 19 July 2025

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1

Kudryashov, Yu L. "Dilatations of Linear Operators." Contemporary Mathematics. Fundamental Directions 66, no. 2 (2020): 209–20. http://dx.doi.org/10.22363/2413-3639-2020-66-2-209-220.

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The article is devoted to building various dilatations of linear operators. The explicit construction of a unitary dilation of a compression operator is considered. Then the J -unitary dilatation of a bounded operator is constructed by means of the operator knot concept of a bounded linear operator. Using the Pavlov method, we construct the self-adjoint dilatation of a bounded dissipative operator. We consider spectral and translational representations of the self-adjoint dilatation of a densely defined dissipative operator with nonempty set of regular points. Using the concept of an operator

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2

Akrym, Abdellah, Abdeslam El Bakkali, and Abdelkhalek Faouzi. "Ergodicity for a family of operators." Boletim da Sociedade Paranaense de Matemática 42 (May 8, 2024): 1–11. http://dx.doi.org/10.5269/bspm.63556.

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The aim of this paper is to introduce the notions of power boundedness, Cesàro boundedness, mean ergodicity, and uniform ergodicity for a family of bounded linear operators on a Banach space. The authors present some elementary results in this setting and show that some main results about power bounded, Cesàro bounded, mean ergodic, and the uniform ergodic operator can be extended from the case of a linear bounded operator to the case of a family of bounded linear operators acting on a Banach space. Also, we show that the Yosida theorem can be extended from the case of a bounded linear operato

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3

Ettayb, Jawad. "(N, ε)-pseudospectra of bounded linear operators on ultrametric Banach spaces". Gulf Journal of Mathematics 17, № 1 (2024): 12–28. http://dx.doi.org/10.56947/gjom.v17i1.1665.

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In this paper, we prove that the essential pseudospectrum of bounded linear operator pencils is invariant under perturbation of completely continuous linear operators on ultrametric Banach spaces over a spherically complete field K and we establish a characterization of the essential pseudospectrum of a bounded linear operator pencils by means of the spectra of all perturbed completely continuous operators. Furthermore, we introduce and study the notion of (n,ε)-pseudospectrum of bounded linear operators and the concept of (n,ε)-pseudospectrum of bounded linear operator pencils on ultrametric

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4

Nakasho, Kazuhisa, Yuichi Futa, and Yasunari Shidama. "Continuity of Bounded Linear Operators on Normed Linear Spaces." Formalized Mathematics 26, no. 3 (2018): 231–37. http://dx.doi.org/10.2478/forma-2018-0021.

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Summary In this article, using the Mizar system [1], [2], we discuss the continuity of bounded linear operators on normed linear spaces. In the first section, it is discussed that bounded linear operators on normed linear spaces are uniformly continuous and Lipschitz continuous. Especially, a bounded linear operator on the dense subset of a complete normed linear space has a unique natural extension over the whole space. In the next section, several basic currying properties are formalized. In the last section, we formalized that continuity of bilinear operator is equivalent to both Lipschitz

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Al-Muttalibi, Rana, and Radhi M.A Ali. "Certain types of linear operators on probabilistic Hilbert space." Global Journal of Mathematical Analysis 3, no. 2 (2015): 81. http://dx.doi.org/10.14419/gjma.v3i2.4664.

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<p>The purpose of this paper is to introduce some definitions, properties and basic results that show the relation between F-bounded of linear operator in probabilistic Hilbert space and bounded operator in norm. In the paper, we prove that the adjoint operator in probabilistic Hilbert space is bounded. The notion of the continuous operators in probabilistic Hilbert space and some basic results are given. In addition, we note that every operator in probabilistic real Hilbert space is a self-adjoint Operator.</p>

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6

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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7

Mohsen, Salim Dawood, and Hanan Khalid Mousa. "Another Results Related of Fuzzy Soft Quasi Normal Operator in Fuzzy Soft Hilbert Space." Journal of Physics: Conference Series 2322, no. 1 (2022): 012050. http://dx.doi.org/10.1088/1742-6596/2322/1/012050.

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Abstract The goal of this paper, is to introduce another classes of the fuzzy soft bounded linear operator in the fuzzy soft Hilbert space which is a fuzzy soft quasi normal operator, as well as, give some properties about this concept with investigating the relationship among this types of the fuzzy soft bounded linear operator on fuzzy soft Hilbert space with other kinds of fuzzy soft bounded linear operators.

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8

Djolović, Ivana, Katarina Petković, and Eberhard Malkowsky. "Matrix mappings and general bounded linear operators on the space bv." Mathematica Slovaca 68, no. 2 (2018): 405–14. http://dx.doi.org/10.1515/ms-2017-0111.

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Abstract If X and Y are FK spaces, then every infinite matrix A ∈ (X, Y) defines a bounded linear operator LA ∈ B(X, Y) where LA(x) = Ax for each x ∈ X. But the converse is not always true. Indeed, if L is a general bounded linear operator from X to Y, that is, L ∈ B(X, Y), we are interested in the representation of such an operator using some infinite matrices. In this paper we establish the representations of the general bounded linear operators from the space bv into the spaces ℓ∞, c and c0. We also prove some estimates for their Hausdorff measures of noncompactness. In this way we show the

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9

Mehd, Sadiq A., Salim Dawood Mohsen, and Mohammed J. Fari. "Properties (RB) and (gRB) for Bounded Linear Operators." Journal of Physics: Conference Series 2322, no. 1 (2022): 012053. http://dx.doi.org/10.1088/1742-6596/2322/1/012053.

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Abstract In this article, we consider pseudo invertible operators for study of the relationship between the space of relatively regular operators and some generalizations of Weyl and Browder theorems. By using the analysis and representation of pseudo invertible operators, some new properties in connection with Browder’s type theorems, were presented for bounded linear operators T ∈ B(X). These properties, which we refer to as property (RB), imply that All poles of the resolvent of T of finite rank in the typical spectrum are precisely those places of the spectrum for which a reasonably regula

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10

ASSADI, AMANOLLAH, MOHAMAD ALI FARZANEH, and HAJI MOHAMMAD MOHAMMADINEJAD. "ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES." Bulletin of the Australian Mathematical Society 99, no. 2 (2019): 274–83. http://dx.doi.org/10.1017/s0004972718001363.

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We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators which have a collection of almost-invariant subspaces and prove that a bounded linear operator on a Banach space, admitting each closed subspace as an almost-invariant subspace, can be decomposed into the sum of a multiple of the identity and a finite-rank operator.

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11

Bajryacharya, Prakash Muni, and Keshab Raj Phulara. "Extension of Bounded Linear Operators." Journal of Advanced College of Engineering and Management 2 (November 29, 2016): 11. http://dx.doi.org/10.3126/jacem.v2i0.16094.

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<p>In this article the problem entitled when does every member of a class of operators T : E → Y admit an extension operator T : X → Y in different approaches like injective spaces, separable injective spaces, the class of compact operators and extension Into C(K ) spaces has-been studied.</p><p><strong>Journal of Advanced College of Engineering and Management,</strong> Vol. 2, 2016, page: 11-13</p>

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12

Liu, Xiaoji, Miao Zhang, and Yaoming Yu. "Note on the Invariance Properties of Operator Products Involving Generalized Inverses." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/213458.

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We investigate further the invariance properties of the bounded linear operator productAC1 B1 Dand its range with respect to the choice of the generalized inversesXandYof bounded linear operators. Also, we discuss the range inclusion invariance properties of the operator product involving generalized inverses.

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13

Frank, Michael. "Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules." Journal of K-theory 2, no. 3 (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 comp

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14

Hejazian, Shirin, Madjid Mirzavaziri, and Omid Zabeti. "Bounded operators on topological vector spaces and their spectral radii." Filomat 26, no. 6 (2012): 1283–90. http://dx.doi.org/10.2298/fil1206283h.

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In this paper, we consider three classes of bounded linear operators on a topological vector space with respect to three different topologies which are introduced by Troitsky. We obtain some properties for the spectral radii of a linear operator on a topological vector space. We find some sufficient conditions for the completeness of these classes of operators. Finally, as a special application, we deduce some sufficient conditions for invertibility of a bounded linear operator.

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15

Yang, Dachun, and Dongyong Yang. "Boundedness of linear operators via atoms on Hardy spaces with non-doubling measures." gmj 18, no. 2 (2011): 377–97. http://dx.doi.org/10.1515/gmj.2011.0018.

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Abstract Let μ be a non-negative Radon measure on which satisfies only the polynomial growth condition. Let 𝒴 be a Banach space and H 1(μ) be the Hardy space of Tolsa. In this paper, the authors prove that a linear operator T is bounded from H 1(μ) to 𝒴 if and only if T maps all (p, γ)-atomic blocks into uniformly bounded elements of 𝒴; moreover, the authors prove that for a sublinear operator T bounded from L 1(μ) to L 1, ∞(μ), if T maps all (p, γ)-atomic blocks with p ∈ (1, ∞) and γ ∈ ℕ into uniformly bounded elements of L 1(μ), then T extends to a bounded sublinear operator from H 1(μ) to L

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16

Topuzu, Elena, and Paul Topuzu. "Remarks on bounded solutions of linear systems." Bulletin of the Australian Mathematical Society 53, no. 3 (1996): 459–67. http://dx.doi.org/10.1017/s0004972700017226.

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In the case of continuous time systems with bounded operators (coefficients) the following result, of Perron type is well known: “The linear differential system ẋ = Ax + f(t) has, for every function f continuous and bounded on ℝ, a unique bounded solution on ℝ, if and only if the spectrum of the operator A has no points on the imaginary axis”.

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17

Brattka, Vasco. "Effective representations of the space of linear bounded operators." Applied General Topology 4, no. 1 (2003): 115. http://dx.doi.org/10.4995/agt.2003.2014.

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<p>Representations of topological spaces by infinite sequences of symbols are used in computable analysis to describe computations in topological spaces with the help of Turing machines. From the computer science point of view such representations can be considered as data structures of topological spaces. Formally, a representation of a topological space is a surjective mapping from Cantor space onto the corresponding space. Typically, one is interested in admissible, i.e. topologically well-behaved representations which are continuous and characterized by a certain maximality condition

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18

Bakery, Awad A. "Operator Ideal of Cesaro Type Sequence Spaces Involving Lacunary Sequence." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/419560.

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The aim of this paper is to give the sufficient conditions on the sequence spaceCesθ,pdefined in Lim (1977) such that the class of all bounded linear operators between any arbitrary Banach spaces withnth approximation numbers of the bounded linear operators inCesθ,pform an operator ideal.

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19

Et al., Kider. "Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces." Baghdad Science Journal 16, no. 1 (2019): 0104. http://dx.doi.org/10.21123/bsj.2019.16.1.0104.

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In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy com

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20

Johnson, P. Sam, and G. Ramu. "Class of bounded operators associated with an atomic system." Tamkang Journal of Mathematics 46, no. 1 (2014): 85–90. http://dx.doi.org/10.5556/j.tkjm.46.2015.1601.

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$K$-frames, more general than the ordinary frames, have been introduced by Laura G{\u{a}}vru{\c{t}}a in Hilbert spaces to study atomic systems with respect to a bounded linear operator. Using the frame operator, we find a class of bounded linear operators in which a given Bessel sequence is an atomic system for every member in the class.

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21

BARNES, BRUCE A. "BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY." Glasgow Mathematical Journal 49, no. 1 (2007): 145–54. http://dx.doi.org/10.1017/s0017089507003503.

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Abstract.LetTbe a bounded linear operator on a Banach spaceW, assumeWandYare in normed duality, and assume thatThas adjointT†relative toY. In this paper, conditions are given that imply that for all λ≠0, λ−Tand λ −T†maintain important standard operator relationships. For example, under the conditions given, λ −Thas closed range if, and only if, λ −T†has closed range.These general results are shown to apply to certain classes of integral operators acting on spaces of continuous functions.

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22

Guesba, Messaoud, та Sid Mahmoud. "On the (α, β)-Euclidean operator radius and its applications". Filomat 38, № 33 (2024): 11593–613. https://doi.org/10.2298/fil2433593g.

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Our aim in this paper is to introduce a new norm of n-tuple operators which generalizes the (?,?)-norm on the space of all bounded linear operators on a complex Hilbert space due to Sain et al. (Ann. Funct. Anal. 12:51 (2021)). We introduce and study basic properties of this norm. As an application of the present study, we estimate bounds for the Euclidean operator radius (joint numerical radius) of bounded linear operators. Also, we improve on some of the important existing Euclidean operator radius inequalities.

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23

Barnes, Bruce A. "A note concerning the ideal of nuclear operators." Glasgow Mathematical Journal 38, no. 2 (1996): 233–36. http://dx.doi.org/10.1017/s0017089500031487.

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24

He, Z., and M. W. Wong. "Wavelet multipliers and signals." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 40, no. 4 (1999): 437–46. http://dx.doi.org/10.1017/s0334270000010523.

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AbstractThe Schatten-von Neumann property of a pseudo-differential operator is established by showing that the pseudo-differential operator is a multiplier defined by means of an admissible wavelet associated to a unitary representation of the additive group Rn on the C*-algebra of all bounded linear operators from L2(Rn) into L2(Rn). A bounded linear operator on L2(R) arising in the Landau, Pollak and Slepian model in signal analysis is shown to be a wavelet multiplier studied in this paper.

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25

Bahreini, Manijeh, Elizabeth Bator, and Ioana Ghenciu. "Complemented Subspaces of Linear Bounded Operators." Canadian Mathematical Bulletin 55, no. 3 (2012): 449–61. http://dx.doi.org/10.4153/cmb-2011-097-2.

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AbstractWe study the complementation of the space W(X, Y) of weakly compact operators, the space K(X, Y) of compact operators, the space U(X, Y) of unconditionally converging operators, and the space CC(X, Y) of completely continuous operators in the space L(X, Y) of bounded linear operators from X to Y. Feder proved that if X is infinite-dimensional and c0 ↪ Y, then K(X, Y) is uncomplemented in L(X, Y). Emmanuele and John showed that if c0 ↪ K(X, Y), then K(X, Y) is uncomplemented in L(X, Y). Bator and Lewis showed that if X is not a Grothendieck space and c0 ↪ Y, then W(X, Y) is uncomplement

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Mezrag, Lahcène, and Abdelmoumene Tiaiba. "On the sublinear operators factoring throughLq." International Journal of Mathematics and Mathematical Sciences 2004, no. 50 (2004): 2695–704. http://dx.doi.org/10.1155/s0161171204303145.

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Let0<p≤q≤+∞. LetTbe a bounded sublinear operator from a Banach spaceXinto anLp(Ω,μ)and let∇Tbe the set of all linear operators≤T. In the present paper, we will show the following. LetCbe a positive constant. For alluin∇T,Cpq(u)≤C(i.e.,uadmits a factorization of the formX→u˜Lq(Ω,μ)→MguLq(Ω,μ), whereu˜is a bounded linear operator with‖u˜‖≤C,Mguis the bounded operator of multiplication byguwhich is inBLr+(Ω,μ)(1/p=1/q+1/r),u=Mgu∘u˜andCpq(u)is the constant ofq-convexity ofu) if and only ifTadmits the same factorization; This is under the supposition that{gu}u∈∇Tis latticially bounded. Without t

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27

Fedorov, V. E., A. D. Godova, and B. T. Kien. "Integro-differential equations with bounded operators in Banach spaces." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 106, no. 2 (2022): 93–107. http://dx.doi.org/10.31489/2022m2/93-107.

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The paper investigates integro-differential equations in Banach spaces with operators, which are a composition of convolution and differentiation operators. Depending on the order of action of these two operators, we talk about integro-differential operators of the Riemann—Liouville type, when the convolution operator acts first, and integro-differential operators of the Gerasimov type otherwise. Special cases of the operators under consideration are the fractional derivatives of Riemann—Liouville and Gerasimov, respectively. The classes of integro-differential operators under study also inclu

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28

Khatskevich, V. A., M. I. Ostrovskii, and V. S. Shulman. "Analogues of the Liouville theorem for linear fractional relations in Banach spaces." Bulletin of the Australian Mathematical Society 73, no. 1 (2006): 89–105. http://dx.doi.org/10.1017/s000497270003865x.

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Consider a bounded linear operator T between Banach spaces ℬ, ℬ′ which can be decomposed into direct sums ℬ = ℬ1 ⌖ ℬ2, ℬ′ = ℬ1′ ⌖ ℬ2′. Such linear operator can be represented by a 2 × 2 operator matrix of the form where Tij ∈ ℒ(ℬj, ℒi′) i, j = 1, 2. (By ℒ(ℬj, ℒi′) we denote the space of bounded linear operators acting from ℬj to ℬi′ (i, j = 1, 2).) The map GT from L (B1, B2) into the set of closed affine subspaces of ℒ(ℬ1′ ℬ2′), defined by is called a linear fractional relation associated with T.Such relations can be considered as a generalisation of linear fractional transformations which wer

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Malkowsky, E., and A. Alotaibi. "Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces." Journal of Function Spaces 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/196489.

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We study the spacesw0p,wp, andw∞pof sequences that are strongly summable to 0, summable, and bounded with indexp≥1by the Cesàro method of order 1 and establish the representations of the general bounded linear operators from the spaceswpinto the spacesw∞1,w1, andw01. We also give estimates for the operator norm and the Hausdorff measure of noncompactness of such operators. Finally we apply our results to characterize the classes of compact bounded linear operators fromw0pandwpintow01andw1.

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SUN, Chenhui, Ning WANG, and Xiaohong CAO. "Topological Uniform Descent and Judgement of A-Weyl's Theorem." Wuhan University Journal of Natural Sciences 28, no. 5 (2023): 392–98. http://dx.doi.org/10.1051/wujns/2023285392.

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In this paper, a-Browder's theorem and a-Weyl's theorem for bounded linear operators are studied by means of the property of the topological uniform descent. The sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space holding a-Browder's theorem and a-Weyl's theorem are established. As a consequence of the main result, the new judgements of a-Browder's theorem and a-Weyl's theorem for operator function are discussed.

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31

Sen, Anirban, Pintu Bhunia, and Kallol Paul. "Bounds for the Berezin number of reproducing kernel Hilbert space operators." Filomat 37, no. 6 (2023): 1741–49. http://dx.doi.org/10.2298/fil2306741s.

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In this paper, we find new upper bounds for the Berezin number of the product of bounded linear operators defined on reproducing kernel Hilbert spaces. We also obtain some interesting upper bounds concerning one operator, the upper bounds obtained here refine the existing ones. Further, we develop new lower bounds for the Berezin number concerning one operator by using their Cartesian decomposition. In particular, we prove that ber(A) ? 1/?2 ber(?(A)? ?(A)1, where ber(A) is the Berezin number of the bounded linear operator A.

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Fomin, Vasiliy I. "About a complex operator resolvent." Russian Universities Reports. Mathematics, no. 138 (2022): 183–97. http://dx.doi.org/10.20310/2686-9667-2022-27-138-183-197.

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A normed algebra of bounded linear complex operators acting in a complex normed space consisting of elements of the Cartesian square of a real Banach space is constructed. In this algebra, it is singled out a set of operators for each of which the real and imaginary parts commute with each other. It is proved that in this set, any operator for which the sum of squares of its real and imaginary parts is a continuously invertible operator, is invertible itself; a formula for the inverse operator is found. For an operator from the indicated set, the form of its regular points is investigated: con

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Amara, Zouheir, Mourad Oudghiri, and Khalid Souilah. "On maps preserving skew symmetric operators." Filomat 36, no. 1 (2022): 243–54. http://dx.doi.org/10.2298/fil2201243a.

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Given a conjugation C on a separable complex Hilbert space H, a bounded linear operator T on H is said to be C-skew symmetric if CTC = -T*. This paper describes the maps, on the algebra of all bounded linear operators acting on H, that preserve the difference of C-skew symmetric operators for every conjugation C on H.

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Azzouz, Abdelhalim, Mahamed Beghdadi, and Bilel Krichen. "Generalized relative essential spectra." Filomat 36, no. 8 (2022): 2657–73. http://dx.doi.org/10.2298/fil2208657a.

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The aim of the present paper is to give some spectral results about generalized Fredholm operators and the so called S-generalized Fredholm operators, where S is a given bounded linear operator acting on a Banach space X. When X possesses some properties, we provide then some sufficient conditions for which a bounded linear operator will be a generalized Fredholm. The obtained results are applied to characterize the so called generalized S-essential spectrum, in particular the generalized Jeribi S-essential spectrum [17]. These results are formulated by means of measure of weak noncompactness.

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35

Sah, Nagendra Pd. "About Riesz theory of compact operators." BIBECHANA 9 (December 10, 2012): 126–29. http://dx.doi.org/10.3126/bibechana.v9i0.7186.

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In this paper, it is shown that every compact operators are bounded and continuous. The bounded and continuous properties of an operator is sufficient for a Riesz operator. For mapping T: K-?I in normed linear space with some extended [1] properties, T becomes compact. DOI: http://dx.doi.org/10.3126/bibechana.v9i0.7186 BIBECHANA 9 (2013) 126-129

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Abdmouleh, Faiçal, and Bilel Elgabeur. "On the pseudo semi-Browder essential spectra and application to 2 × 2 block operator matrices." Filomat 37, no. 19 (2023): 6373–86. http://dx.doi.org/10.2298/fil2319373a.

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In the present paper, we introduce and study the pseudo semi-Browder essential spectra of bounded linear operators in a Banach space. We start by defining the pseudo semi-Browder operators and we prove the stability of these operators under commuting Riesz operator perturbations. Then, we apply the obtained results to study the stability of the pseudo semi-Browder essential spectra. We show as well the relation between the pseudo semi-Browder spectrum of the sum of two bounded linear operators and the pseudo semi-Browder spectrum of each of these operators. As an application, we study the pseu

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Ge, Zhaoqiang. "Linear Quadratic Optimal Control Problem for Linear Stochastic Generalized System in Hilbert Spaces." Mathematics 10, no. 17 (2022): 3118. http://dx.doi.org/10.3390/math10173118.

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A finite-horizon linear stochastic quadratic optimal control problem is investigated by the GE-evolution operator in the sense of the MILS solution in Hilbert spaces. We assume that the coefficient operator of the differential term is a bounded linear operator and that the state and input operators are time-varying in the dynamic equation of the problem. Optimal state feedback along with the well-posedness of the generalized Riccati equation is obtained for the finite-horizon case. The results are also applicable to the linear quadratic optimal control problem of ordinary time-varying linear s

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38

Przyłuski, K. Maciej. "On a discrete-time version of a problem of A. J. Pritchard and J. Zabczyk." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 101, no. 1-2 (1985): 159–61. http://dx.doi.org/10.1017/s0308210500026251.

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SynopsisIt is shown that every weakly l1-stable linear and bounded operator (which represents a linear discrete-time system) on a Hilbert space is power stable. It solves (at least partially) a discrete-time version of a problem posed by A. J. Pritchard and J. Zabczyk for strongly continuous semigroups of bounded linear operators.

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39

Feng, Gaohuizi, and Pengtong Li. "Weyl type theorem and its perturbations for bounded linear operators." Filomat 38, no. 22 (2024): 7683–92. https://doi.org/10.2298/fil2422683f.

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As two variations of Weyl?s theorem, a-Weyl?s theorem and property (?) are introduced by Rakocevic. In this paper, we study a-Weyl?s theorem and property (?) for functions of bounded linear operators. And concrete examples are given to show that the two properties are independent of each other. We give the necessary and sufficient condition for a bounded linear operator with both a-Weyl?s theorem and property (?) utilizing the induced spectrum of topological uniform descent. Also, we investigate the perturbations of operator functions satisfying both a-Weyl?s theorem and property (?).

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Yurdakul, Murat, та Emre Taştüner. "Bounded factorization property for ℓ-Köthe spaces". Filomat 37, № 11 (2023): 3631–37. https://doi.org/10.2298/fil2311631y.

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Let ? denote a Banach sequence space with a monotone norm in which the canonical system (en)n is an unconditional basis. We show that the existence of an unbounded continuous linear operator T between ?-K?the spaces ??(A) and ??(C) which factors through a third ?-K?the space ??(B) causes the existence of an unbounded continuous quasidiagonal operator from ??(A) into ??(C) factoring through ??(B) as a product of two continuous quasidiagonal operators. Using this result, we study when the triple (??(A), ??(B), ??(C)) satisfies the bounded factorization property BF (which means that all continuou

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WARK, H. M. "A NON-SEPARABLE REFLEXIVE BANACH SPACE ON WHICH THERE ARE FEW OPERATORS." Journal of the London Mathematical Society 64, no. 3 (2001): 675–89. http://dx.doi.org/10.1112/s0024610701002393.

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It is shown that there exists a non-separable reflexive Banach space on which every bounded linear operator is the sum of a scalar multiple of the identity operator and an operator of separable range. There is a strong sense that such a Banach space has as few operators as its linear and topological properties allow.

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An, Il, and Jaeseong Heo. "Weyl type theorems for selfadjoint operators on Krein spaces." Filomat 32, no. 17 (2018): 6001–16. http://dx.doi.org/10.2298/fil1817001a.

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In this paper, we introduce a notion of the J-kernel of a bounded linear operator on a Krein space and study the J-Fredholm theory for Krein space operators. Using J-Fredholm theory, we discuss when (a-)J-Weyl?s theorem or (a-)J-Browder?s theorem holds for bounded linear operators on a Krein space instead of a Hilbert space.

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Luketero, S. W., B. M. Nzimbi, and S. K. Moindi. "On Intertwining and Quasi-Affine Sets of Operators." IOSR Journal of Mathematics 20, no. 5 (2024): 01–09. http://dx.doi.org/10.9790/5728-2005010109.

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In this paper, we investigate some intertwining sets and quasi-affine sets of some classes of operators in Hilbert spaces. We are interested in the intertwining relation of the form WX = XR, where W, R are some bounded linear operators and X is an arbitrary bounded linear operator which we will endow some special properties. 2010 Mathematics Subject Classification: Primary 47A05,47A11; Secondary 47B20,47A65

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Smati, A., and M. Guesba. "On the classes of $n$-Nadir's and $n^*$-Nadir's operators on Hilbert spaces." Carpathian Mathematical Publications 17, no. 1 (2025): 137–45. https://doi.org/10.15330/cmp.17.1.137-145.

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The main aim of this paper is to present some new results for Nadir's operator $N=AB^{*}-BA^{*}$, where $A$ and $B$ are two bounded linear operators. We introduce a generalization of this concept, that is, the $n$-Nadir's and $n^*$-Nadir's operators, where $n$ is a positive integer. We present fundamental properties of these operators, including compactness and normality. Additionally, we establish relationships between these classes, we show that the adjoint of $n$-Nadir's operator is $n^*$-Nadir's operator. Furthermore, if $T$ is an $n$-Nadir's operator, such that $ A $ and $ B $ are two bou

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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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Altwaijry, Najla, Silvestru Sever Dragomir, and Kais Feki. "Inequalities and Reverse Inequalities for the Joint A-Numerical Radius of Operators." Axioms 12, no. 3 (2023): 316. http://dx.doi.org/10.3390/axioms12030316.

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In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space H, which leads to the special case of the well-known A-numerical radius for d=1. Here, A is a positive operator on H. Some inequalities related to the Euclidean operator A-seminorm of d-tuples of A-bounded operators are proved. In addition, under appropriate conditions, several reverse bounds for the A-numerical radius in single and multivariable settings are also stated.

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TERAUDS, VENTA. "FUNCTIONAL CALCULUS EXTENSIONS ON DUAL SPACES." Bulletin of the Australian Mathematical Society 79, no. 1 (2009): 71–77. http://dx.doi.org/10.1017/s0004972708001032.

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AbstractIn this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this result is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply our theorem to give some sufficient conditions for an operator with an absolutely continuous functional calculus to admit a bounded Borel one.

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Gau, Haw-Long, Jyh-Shyang Jeang, and Nagi-Ching Wong. "Biseparating linear maps between continuous vector-valued function spaces." Journal of the Australian Mathematical Society 74, no. 1 (2003): 101–10. http://dx.doi.org/10.1017/s1446788700003153.

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AbstractLet X, Y be compact Hausdorff spaces and E, F be Banach spaces. A linear map T: C(X, E) → C(Y, F) is separating if Tf, Tg have disjoint cozeroes whenever f, g have disjoint cozeroes. We prove that a biseparating linear bijection T (that is, T and T-1 are separating) is a weighted composition operator Tf = h · f o ϕ. Here, h is a function from Y into the set of invertible linear operators from E onto F, and ϕ, is a homeomorphism from Y onto X. We also show that T is bounded if and only if h(y) is a bounded operator from E onto F for all y in Y. In this case, h is continuous with respect

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Ammar, Aymen, Ameni Bouchekoua, and Aref Jeribi. "A characterization of S-pseudospectra of linear operators in a Hilbert space." Filomat 37, no. 5 (2023): 1331–39. http://dx.doi.org/10.2298/fil2305331a.

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In this work, we introduce and study the S-pseudospectra of linear operators defined by nonstrict inequality in a Hilbert space. Inspired by A. B?ttcher?s result [3], we prove that the S-resolvent norm of bounded linear operators is not constant in any open set of the S-resolvent set. Beside, we find a characterization of the S-pseudospectrum of bounded linear operator by means the S-spectra of all perturbed operators with perturbations that have norms strictly less than ?.

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Liu, Ming, and Xia Zhang. "L0-Linear Modulus of a Random Linear Operator." Abstract and Applied Analysis 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/183197.

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