The Experts below are selected from a list of 15228 Experts worldwide ranked by ideXlab platform
Debmalya Sain - One of the best experts on this subject based on the ideXlab platform.
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level numbers of a Bounded Linear Operator between normed Linear spaces and singular value decomposition revisited
Linear & Multilinear Algebra, 2020Co-Authors: Debmalya Sain, Saikat Roy, Ryotaro TanakaAbstract:We introduce the notion of level numbers of a Bounded Linear Operator between normed Linear spaces, as a generalization of the singular values of an Operator between inner product spaces. We study ...
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on the norm attainment set of a Bounded Linear Operator and semi inner products in normed spaces
Indian Journal of Pure & Applied Mathematics, 2020Co-Authors: Debmalya SainAbstract:We obtain a complete characterization of the norm attainment set of a Bounded Linear Operator between normed spaces, in terms of semi-inner-product(s) defined on the space. In particular, this answers an open question raised recently in D. Sain, On the norm attainment set of a Bounded Linear Operator, J. Math. Anal. Appl., 457 (2018), 67�76. Our results illustrate the applicability of semi-inner-products towards a better understanding of the geometry of normed spaces. © 2020, Indian National Science Academy.
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on the norm attainment set of a Bounded Linear Operator and semi inner products in normed spaces
Indian Journal of Pure & Applied Mathematics, 2020Co-Authors: Debmalya SainAbstract:We obtain a complete characterization of the norm attainment set of a Bounded Linear Operator between normed spaces, in terms of semi-inner-product(s) defined on the space. In particular, this answers an open question raised recently in [D. Sain, On the norm attainment set of a Bounded Linear Operator, J. Math. Anal. Appl., 457 (2018), 67–76]. Our results illustrate the applicability of semi-inner-products towards a better understanding of the geometry of normed spaces.
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On numerical radius and Crawford number attainment sets of a Bounded Linear Operator.
arXiv: Functional Analysis, 2020Co-Authors: Debmalya Sain, Arpita Mal, Pintu Bhunia, Kallol PaulAbstract:We completely characterize the Crawford number attainment set and the numerical radius attainment set of a Bounded Linear Operator on a Hilbert space. We study the intersection properties of the corresponding attainment sets of numerical radius, Crawford number, norm, minimum norm of a Bounded Linear Operator defined on a normed space. Our study illustrates the similarities and the differences of the extremal properties of a Bounded Linear Operator on a Hilbert space and a general normed space.
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on two extremum problems related to the norm of a Bounded Linear Operator
Operators and Matrices, 2019Co-Authors: Debmalya Sain, Kallol Paul, Kalidas MandalAbstract:We explore the norm attainment set and the minimum norm attainment set of a Bounded Linear Operator between Hilbert spaces and Banach spaces. Indeed, we obtain a complete characterization of both the sets, separately for Operators between Hilbert spaces and Banach spaces. We also study the interconnection between these two sets and prove that for Operators between Hilbert spaces, these two sets are either equal or mutually orthogonal, provided both of them are non-empty. We also obtain separate complete characterizations of reflexive Banach spaces and Euclidean spaces in terms of the norm (minimum norm) attainment set, in order to illustrate the importance of our study.
Lalit K. Vashisht - One of the best experts on this subject based on the ideXlab platform.
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\(\mathcal {K}\)-Matrix-valued Wave Packet Frames in \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\)
2018Co-Authors: Jyoti, Lalit K. VashishtAbstract:We study frame properties of a matrix-valued wave packet system in the matrix-valued function space \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\), where the lower frame condition is controlled by a Bounded Linear Operator \(\mathcal {K}\) on \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\) (lower \(\mathcal {K}\)-frame condition, in short). There are many differences between ordinary frames and \(\mathcal {K}\)-frames. The lower \(\mathcal {K}\)-frame condition for matrix-valued wave packet Bessel sequences in \(L^{2}(\mathbb {R}^{d},\mathbb {C}^{s\times r})\) in terms of Operators; a trace functional associated with a Bounded Linear Operator on \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\); and a series associated with a matrix-valued Bessel sequence is presented. It is shown that matrix-valued wave packet frames are stable under small perturbation with respect to wave packet window functions.
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$\mathcal {}$-Matrix-valued Wave Packet Frames in L2(ℝd,ℂs×r)$L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})$
Mathematical Physics Analysis and Geometry, 2018Co-Authors: Jyoti, Lalit K. VashishtAbstract:We study frame properties of a matrix-valued wave packet system in the matrix-valued function space \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\), where the lower frame condition is controlled by a Bounded Linear Operator \(\mathcal {K}\) on \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\) (lower \(\mathcal {K}\)-frame condition, in short). There are many differences between ordinary frames and \(\mathcal {K}\)-frames. The lower \(\mathcal {K}\)-frame condition for matrix-valued wave packet Bessel sequences in \(L^{2}(\mathbb {R}^{d},\mathbb {C}^{s\times r})\) in terms of Operators; a trace functional associated with a Bounded Linear Operator on \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\); and a series associated with a matrix-valued Bessel sequence is presented. It is shown that matrix-valued wave packet frames are stable under small perturbation with respect to wave packet window functions.
Spiros A. Argyros - One of the best experts on this subject based on the ideXlab platform.
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a reflexive hereditarily indecomposable space with the hereditary invariant subspace property
Proceedings of The London Mathematical Society, 2014Co-Authors: Spiros A. Argyros, Pavlos MotakisAbstract:A reflexive hereditarily indecomposable Banach space XISP is presented, such that for every Y infinite dimensional closed subspace of XISP and every Bounded Linear Operator T : Y ! Y , the Operator T admits a non-trivial closed invariant subspace.
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a reflexive hi space with the hereditary invariant subspace property
arXiv: Functional Analysis, 2011Co-Authors: Spiros A. Argyros, Pavlos MotakisAbstract:A reflexive hereditarily indecomposable Banach space XISP is presented, such that for every Y infinite dimensional closed subspace of XISP and every Bounded Linear Operator T : Y ! Y , the Operator T admits a non-trivial closed invariant subspace.
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a hereditarily indecomposable mathcal l _ infty space that solves the scalar plus compact problem
Acta Mathematica, 2011Co-Authors: Spiros A. Argyros, Richard HaydonAbstract:We construct a hereditarily indecomposable Banach space with dual space isomorphic to l 1. Every Bounded Linear Operator on this space is expressible as λI + K, with λ a scalar and K compact.
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A hereditarily indecomposable $ {\mathcal{L}_{\infty}} $ -space that solves the scalar-plus-compact problem
Acta Mathematica, 2011Co-Authors: Spiros A. Argyros, Richard G. HaydonAbstract:We construct a hereditarily indecomposable Banach space with dual space isomorphic to ℓ _1. Every Bounded Linear Operator on this space is expressible as λ I + K , with λ a scalar and K compact.
Aziz Abdul - One of the best experts on this subject based on the ideXlab platform.
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NORMA Operator PADA RUANG FUNGSI TERINTEGRAL DUNFORD
'Institute of Research and Community Services Diponegoro University (LPPM UNDIP)', 2019Co-Authors: Solikhin Solikhin, Hariyanto Susilo, Sumanto Y.d., Aziz AbdulAbstract:We are discussed Operator norms on spce of Dunford integral function. We show that for a function which Dunford integral, Operator from dual space into space of Lebesgue integral is a Bounded Linear Operator. Furthermore, sets of all Bounded Linear Operator is a Linear space and it is a normed space by norm certain. Finally, the distance function generated by the norm is metrix space
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NORMA Operator PADA RUANG FUNGSI TERINTEGRAL DUNFORD
Department of Mathematics Faculty of Science and Mathematics Diponegoro University, 2019Co-Authors: Solikhin Solikhin, Hariyanto Susilo, Yd Sumanto, Aziz AbdulAbstract:Abstrack. We are discussed Operator norms on spce of Dunford integral function. We show that for a function which Dunford integral, Operator from dual space into space of Lebesgue integral is a Bounded Linear Operator. Furthermore, sets of all Bounded Linear Operator is a Linear space and it is a normed space by norm certain. Finally, the distance function generated by the norm is metrix space. Abstrak. Artikel ini membahas Operator pada ruang fungsi terintegral Dunford. Ditunjukkan bahwa untuk setiap fungsi yang terintegral Dunford, Operator dari ruang dual ke ruang integral Lebesgue merupakan Operator Linear terbatas. Selanjutnya himpunan semua Operator Linear terbatas merupakan ruang Linear dan dengan norma tertentu merupakan ruang bernorma. Lebih lanjut dengan fungsi jarak yang dibangkitkan dari normanya merupakan ruang metrik.
Jyoti - One of the best experts on this subject based on the ideXlab platform.
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\(\mathcal {K}\)-Matrix-valued Wave Packet Frames in \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\)
2018Co-Authors: Jyoti, Lalit K. VashishtAbstract:We study frame properties of a matrix-valued wave packet system in the matrix-valued function space \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\), where the lower frame condition is controlled by a Bounded Linear Operator \(\mathcal {K}\) on \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\) (lower \(\mathcal {K}\)-frame condition, in short). There are many differences between ordinary frames and \(\mathcal {K}\)-frames. The lower \(\mathcal {K}\)-frame condition for matrix-valued wave packet Bessel sequences in \(L^{2}(\mathbb {R}^{d},\mathbb {C}^{s\times r})\) in terms of Operators; a trace functional associated with a Bounded Linear Operator on \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\); and a series associated with a matrix-valued Bessel sequence is presented. It is shown that matrix-valued wave packet frames are stable under small perturbation with respect to wave packet window functions.
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$\mathcal {}$-Matrix-valued Wave Packet Frames in L2(ℝd,ℂs×r)$L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})$
Mathematical Physics Analysis and Geometry, 2018Co-Authors: Jyoti, Lalit K. VashishtAbstract:We study frame properties of a matrix-valued wave packet system in the matrix-valued function space \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\), where the lower frame condition is controlled by a Bounded Linear Operator \(\mathcal {K}\) on \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\) (lower \(\mathcal {K}\)-frame condition, in short). There are many differences between ordinary frames and \(\mathcal {K}\)-frames. The lower \(\mathcal {K}\)-frame condition for matrix-valued wave packet Bessel sequences in \(L^{2}(\mathbb {R}^{d},\mathbb {C}^{s\times r})\) in terms of Operators; a trace functional associated with a Bounded Linear Operator on \(L^{2}(\mathbb {R}^{d}, \mathbb {C}^{s\times r})\); and a series associated with a matrix-valued Bessel sequence is presented. It is shown that matrix-valued wave packet frames are stable under small perturbation with respect to wave packet window functions.