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Journal articles on the topic 'Bounded linear operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Rashid, M. H. M. "Propertiesandfor Bounded Linear Operators." Journal of Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/848176.

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We shall consider properties which are related to Weyl type theorem for bounded linear operators , defined on a complex Banach space . These properties, that we callproperty, means that the set of all poles of the resolvent of of finite rank in the usual spectrum are exactly those points of the spectrum for which is an upper semi-Fredholm with index less than or equal to 0 and we callproperty, means that the set of all poles of the resolvent of in the usual spectrum are exactly those points of the spectrum for which is an upper semi--Fredholm with index less than or equal to 0. Properties and are related to a strong variants of classical Weyl’s theorem, the so-called property and property We shall characterize properties and in several ways and we shall also describe the relationships of it with the other variants of Weyl type theorems. Our main tool is localized version of the single valued extension property. Also, we consider the properties and in the frame of polaroid type operators.

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2

Bag, T., and S. K. Samanta. "Fuzzy bounded linear operators." Fuzzy Sets and Systems 151, no. 3 (May 2005): 513–47. http://dx.doi.org/10.1016/j.fss.2004.05.004.

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3

Ghosh, Puja, Debmalya Sain, and Kallol Paul. "Orthogonality of bounded linear operators." Linear Algebra and its Applications 500 (July 2016): 43–51. http://dx.doi.org/10.1016/j.laa.2016.03.009.

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4

Jasim, Muna, and Manal Ali. "Modules and Bounded Linear Operators." Journal of Al-Nahrain University-Science 19, no. 1 (March 2016): 168–72. http://dx.doi.org/10.22401/jnus.19.1.19.

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5

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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6

Kudryashov, Yu L. "Dilatations of Linear Operators." Contemporary Mathematics. Fundamental Directions 66, no. 2 (December 15, 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 knot for a bounded operator and the Cayley transform, we introduce an operator knot for a linear operator. By means of this concept, we construct the J -self-adjoint dilatation of a densely defined operator with a regular point. We obtain conditions of isomorphism of extraneous dilations and their minimality.

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7

Baskakov, A. G. "Linear differential operators with unbounded operator coefficients and semigroups of bounded operators." Mathematical Notes 59, no. 6 (June 1996): 586–93. http://dx.doi.org/10.1007/bf02307207.

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8

Bahreini, Manijeh, Elizabeth Bator, and Ioana Ghenciu. "Complemented Subspaces of Linear Bounded Operators." Canadian Mathematical Bulletin 55, no. 3 (September 1, 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 uncomplemented in L(X, Y). In this paper, classical results of Kalton and separably determined operator ideals with property (∗) are used to obtain complementation results that yield these theorems as corollaries.

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9

Jung, W., R. Metzger, C. A. Morales, and H. Villavicencio. "A distance between bounded linear operators." Topology and its Applications 284 (October 2020): 107359. http://dx.doi.org/10.1016/j.topol.2020.107359.

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10

Xiao, Xiang-chun, Yu-can Zhu, Zhi-biao Shu, and Ming-ling Ding. "G-frames with bounded linear operators." Rocky Mountain Journal of Mathematics 45, no. 2 (April 2015): 675–93. http://dx.doi.org/10.1216/rmj-2015-45-2-675.

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11

Lili, Zang, and Sun Wenchang. "Invertible sequences of bounded linear operators." Acta Mathematica Scientia 31, no. 5 (September 2011): 1939–44. http://dx.doi.org/10.1016/s0252-9602(11)60372-x.

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12

Shakhmatov, Dmitri, Vesko Valov, and Takamitsu Yamauchi. "Linear extension operators of bounded norms." Journal of Mathematical Analysis and Applications 466, no. 1 (October 2018): 952–60. http://dx.doi.org/10.1016/j.jmaa.2018.06.030.

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13

Rashid, M. H. M., and T. Prasad. "Property (Sw) for bounded linear operators." Asian-European Journal of Mathematics 08, no. 01 (March 2015): 1550012. http://dx.doi.org/10.1142/s1793557115500126.

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14

Xu, Xiao Ming, Hong Ke Du, and Xiao Chun Fang. "Γ-inverses of bounded linear operators." Acta Mathematica Sinica, English Series 30, no. 4 (May 16, 2013): 675–80. http://dx.doi.org/10.1007/s10114-013-2552-y.

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15

Aiena, Pietro, Jesús R. Guillén, and Pedro Peña. "Property (R) for Bounded Linear Operators." Mediterranean Journal of Mathematics 8, no. 4 (February 19, 2011): 491–508. http://dx.doi.org/10.1007/s00009-011-0113-0.

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16

Sebastian, Sabu, and Kiran Kumar. "Real Powers of Bounded Linear Operators." International Journal of Applied and Computational Mathematics 3, no. 2 (November 18, 2015): 645–50. http://dx.doi.org/10.1007/s40819-015-0114-y.

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17

Puglisi, D., and J. B. Seoane-Sepúlveda. "Bounded linear non-absolutely summing operators." Journal of Mathematical Analysis and Applications 338, no. 1 (February 2008): 292–98. http://dx.doi.org/10.1016/j.jmaa.2007.05.029.

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18

Rogers, Robert R. "Triangular form for bounded linear operators." Journal of Functional Analysis 88, no. 1 (January 1990): 135–52. http://dx.doi.org/10.1016/0022-1236(90)90122-2.

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19

Vasanthakumar, P., and N. Jayanthi. "PROPERTY (Bv) FOR BOUNDED LINEAR OPERATORS." International Journal of Functional Analysis, Operator Theory and Applications 13, no. 1 (March 15, 2021): 57–66. http://dx.doi.org/10.17654/fa013010057.

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20

Rano, Gobardhan, and Tarapada Bag. "Bounded linear operators in quasi-normed linear space." Journal of the Egyptian Mathematical Society 23, no. 2 (July 2015): 303–8. http://dx.doi.org/10.1016/j.joems.2014.06.003.

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21

Nakasho, Kazuhisa, Yuichi Futa, and Yasunari Shidama. "Continuity of Bounded Linear Operators on Normed Linear Spaces." Formalized Mathematics 26, no. 3 (October 1, 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 continuity and local continuity. We referred to [4], [13], and [3] in this formalization.

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22

Saccoman, John J. "On the extension of linear operators." International Journal of Mathematics and Mathematical Sciences 28, no. 10 (2001): 621–23. http://dx.doi.org/10.1155/s0161171201006998.

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It is well known that the Hahn-Banach theorem, that is, the extension theorem for bounded linear functionals, is not true in general for bounded linear operators. A characterization of spaces for which it is true was published by Kakutani in 1940. We summarize Kakutani's work and we give an example which demonstrates that his characterization is not valid for two-dimensional spaces.

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23

Lee, Sang Hoon, Woo Young Lee, and Jasang Yoon. "The mean transform of bounded linear operators." Journal of Mathematical Analysis and Applications 410, no. 1 (February 2014): 70–81. http://dx.doi.org/10.1016/j.jmaa.2013.08.003.

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24

Xu, Hong-Kun, and Isao Yamada. "ASYMPTOTIC REGULARITY OF LINEAR POWER BOUNDED OPERATORS." Taiwanese Journal of Mathematics 10, no. 2 (February 2006): 417–29. http://dx.doi.org/10.11650/twjm/1500403834.

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25

Haagerup, Uffe, and Gilles Pisier. "Bounded linear operators between $C^\ast$ -algebras." Duke Mathematical Journal 71, no. 3 (September 1993): 889–925. http://dx.doi.org/10.1215/s0012-7094-93-07134-7.

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26

NISHISHIRAHO, Toshihiko. "Saturation of iterations of bounded linear operators." Hokkaido Mathematical Journal 18, no. 2 (June 1989): 273–84. http://dx.doi.org/10.14492/hokmj/1381517764.

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27

Smith, Richard J. "Bounded linear Talagrand operators on ordinal spaces." Quarterly Journal of Mathematics 56, no. 3 (September 1, 2005): 383–95. http://dx.doi.org/10.1093/qmath/hah038.

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28

Barnes, Bruce A. "Restrictions of bounded linear operators: Closed range." Proceedings of the American Mathematical Society 135, no. 6 (November 15, 2006): 1735–40. http://dx.doi.org/10.1090/s0002-9939-06-08624-2.

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29

Nakasho, Kazuhisa. "Bilinear Operators on Normed Linear Spaces." Formalized Mathematics 27, no. 1 (April 1, 2019): 15–23. http://dx.doi.org/10.2478/forma-2019-0002.

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Summary The main aim of this article is proving properties of bilinear operators on normed linear spaces formalized by means of Mizar [1]. In the first two chapters, algebraic structures [3] of bilinear operators on linear spaces are discussed. Especially, the space of bounded bilinear operators on normed linear spaces is developed here. In the third chapter, it is remarked that the algebraic structure of bounded bilinear operators to a certain Banach space also constitutes a Banach space. In the last chapter, the correspondence between the space of bilinear operators and the space of composition of linear opearators is shown. We referred to [4], [11], [2], [7] and [8] in this formalization.

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30

Malkowsky, Eberhard. "Some Compact Operators on the Hahn Space." Scientific Research Communications 1, no. 1 (July 29, 2021): 1–14. http://dx.doi.org/10.52460/src.2021.001.

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We establish the characterisations of the classes of bounded linear operators from the generalised Hahn sequence space hd, where d is an unbounded monotone increasing sequence of positive real numbers, into the spaces [c0], [c] and [c1] of sequences that are strongly convergent to zero, strongly convergent and strongly bounded. Furthermore, we prove estimates for the Hausdor_ measure of noncompactness of bounded linear operators from hd into [c], and identities for the Hausdor_ measure of noncompactness of bounded linear operators from hd to [c0], and use these results to characterise the classes of compact operators from hd to [c] and [c0].

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31

Brešar, Matej, and Peter Šemrl. "Normal-Preserving Linear Mappings." Canadian Mathematical Bulletin 37, no. 3 (September 1, 1994): 306–9. http://dx.doi.org/10.4153/cmb-1994-046-1.

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32

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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33

Cho, Chong-Man. "Spaces of compact operators which areM-ideals inL(X,Y)." International Journal of Mathematics and Mathematical Sciences 15, no. 3 (1992): 617–19. http://dx.doi.org/10.1155/s0161171292000802.

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SupposeXandYare reflexive Banach spaces. IfK(X,Y), the space of all compact linear operaters fromXtoYis anM-ideal inL(X,Y), the space of all bounded linear operators fromXtoY, then the second dual spaceK(X,Y)**ofK(X,Y)is isometrically isomorphic toL(X,Y).

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34

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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35

Minculete, Nicuşor. "About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators." Symmetry 13, no. 2 (February 11, 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 bounded linear operators on a Hilbert space. Finally, we present several applications of some identities for Hermitian operators.

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36

Saksman, Eero, and Hans-olav Tylli. "Weak Compactness of Multiplication Operators on Spaces of Bounded Linear Operators." MATHEMATICA SCANDINAVICA 70 (June 1, 1992): 91. http://dx.doi.org/10.7146/math.scand.a-12388.

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37

Swartz, Charles. "The uniform boundedness principle for order bounded operators." International Journal of Mathematics and Mathematical Sciences 12, no. 3 (1989): 487–92. http://dx.doi.org/10.1155/s0161171289000621.

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Under appropriate hypotheses on the spaces, it is shown that a sequence of order bounded linear operators which is pointwise order bounded is uniformly order bounded on order bounded subsets. This result is used to establish a Banach-Steinhaus Theorem for order bounded operators.

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38

Khan, Vakeel A., Ayhan Esi, Mobeen Ahmad, and Mohammad Daud Khan. "Continuous and bounded linear operators in neutrosophic normed spaces." Journal of Intelligent & Fuzzy Systems 40, no. 6 (June 21, 2021): 11063–70. http://dx.doi.org/10.3233/jifs-202189.

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In this article, we show that the addition and scalar multiplication in neutrosophic normed spaces are continuous. The neutrosophic boundedness and continuity of linear operators between neutrosophic normed spaces are examined. Moreover, we analyzed that the set of all neutrosophic continuous linear operators and the set of all neutrosophic bounded linear operators from neutrosophic normed spaces into another are vector spaces.

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39

AIENA, Pietro, Muneo CHŌ, and Lingling ZHANG. "Weyl's Theorems and Extensions of Bounded Linear Operators." Tokyo Journal of Mathematics 35, no. 2 (December 2012): 279–89. http://dx.doi.org/10.3836/tjm/1358951318.

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40

Kusraev, A. G., and Z. A. Kusraeva. "Sums of order bounded disjointness preserving linear operators." Sibirskii matematicheskii zhurnal 60, no. 1 (June 8, 2018): 148–61. http://dx.doi.org/10.33048/smzh.2019.60.113.

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41

Carpintero, C., E. Rosas, J. Rodriguez, D. Muñoz, and K. Alcalá. "Spectral properties and restrictions of bounded linear operators." Annals of Functional Analysis 6, no. 2 (2015): 173–83. http://dx.doi.org/10.15352/afa/06-2-15.

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42

Sanabria, J., C. Carpintero, E. Rosas, and O. García. "On generalized property (v) for bounded linear operators." Studia Mathematica 212, no. 2 (2012): 141–54. http://dx.doi.org/10.4064/sm212-2-3.

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43

Léka, Zoltán. "On time regularity properties of bounded linear operators." Banach Center Publications 112 (2017): 211–20. http://dx.doi.org/10.4064/bc112-0-12.

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44

Aiyub, M. "Bounded linear operators for some new matrix transformations." Proyecciones (Antofagasta) 31, no. 3 (September 2012): 209–17. http://dx.doi.org/10.4067/s0716-09172012000300002.

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45

BARNES, BRUCE A. "BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY." Glasgow Mathematical Journal 49, no. 1 (January 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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46

Rashid, M. H. M. "Properties (S) and (gS) for bounded linear operators." Filomat 28, no. 8 (2014): 1641–52. http://dx.doi.org/10.2298/fil1408641r.

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An operator T acting on a Banach space X obeys property (R) if ?0a(T) = E0(T), where ?0a(T) is the set of all left poles of T of finite rank and E0(T) is the set of all isolated eigenvalues of T of finite multiplicity. In this paper we introduce and study two new properties (S) and (gS) in connection with Weyl type theorems. Among other things, we prove that if T is a bounded linear operator acting on a Banach space, then T satisfies property (R) if and only if T satisfies property (S) and ?0(T) = ?0a(T), where ?0(T) is the set of poles of finite rank. Also we show if T satisfies Weyl theorem, then T satisfies property (S). Analogous results for property (gS) are given. Moreover, these properties are also studied in the frame of polaroid operator.

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47

Lewandowska, Zofia. "Bounded 2-linear operators on 2-normed sets." Glasnik Matematicki 39, no. 2 (December 15, 2004): 301–12. http://dx.doi.org/10.3336/gm.39.2.11.

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48

Malinen, J., O. Nevanlinna, and Z. Yuan. "ON A TAUBERIAN CONDITION FOR BOUNDED LINEAR OPERATORS." Mathematical Proceedings of the Royal Irish Academy 109, no. 1 (January 1, 2009): 101–8. http://dx.doi.org/10.3318/pria.2008.109.1.101.

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49

Ok, Efe A. "Nonzero fixed points of power-bounded linear operators." Proceedings of the American Mathematical Society 131, no. 5 (September 19, 2002): 1539–51. http://dx.doi.org/10.1090/s0002-9939-02-06740-0.

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50

Kusraev, A. G., and Z. A. Kusraeva. "Sums of Order Bounded Disjointness Preserving Linear Operators." Siberian Mathematical Journal 60, no. 1 (January 2019): 114–23. http://dx.doi.org/10.1134/s0037446619010130.

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