Zobrazeno 1 - 10
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pro vyhledávání: '"Sain, Debmalya"'
Autor:
Sain, Debmalya
Publikováno v:
RACSAM 115, 120 (2021).
We study the concepts of orthogonality and smoothness in normed linear spaces, induced by the derivatives of the norm function. We obtain analytic characterizations of the said orthogonality relations in terms of support functionals in the dual space
Externí odkaz:
http://arxiv.org/abs/2408.00708
Autor:
Sain, Debmalya
We study a local version of the ball-covering problem in Banach spaces, and obtain a complete solution to it in terms of the norm derivatives. We illustrate the advantage of the local approach by obtaining substantial refinements of several previousl
Externí odkaz:
http://arxiv.org/abs/2408.00685
Publikováno v:
Linear Multilinear Algebra, 72 (1), (2022), 31-49
We study the best coapproximation problem in the Banach space $ \ell_1^n, $ by using Birkhoff-James orthogonality techniques. Given a subspace $\mathbb{{Y}}$ of $\ell_1^n$, we completely identify the elements $x$ in $\ell_1^n,$ for which best coappro
Externí odkaz:
http://arxiv.org/abs/2407.20102
Publikováno v:
Linear Multilinear Algebra, 71(1), (2021), 47-62
We characterize the best coapproximation(s) to a given matrix $ T $ out of a given subspace $ \mathbb{Y} $ of the space of diagonal matrices $ \mathcal{D}_n $, by using Birkhoff-James orthogonality techniques and with the help of a newly introduced p
Externí odkaz:
http://arxiv.org/abs/2407.20096
Publikováno v:
Bull. Sci. Math.196 (2024), 103486
We explore the $k$-smoothness of bounded linear operators between Banach spaces, using the newly introduced notion of index of smoothness. The characterization of the $k$-smoothness of operators between Hilbert spaces follows as a direct consequence
Externí odkaz:
http://arxiv.org/abs/2407.19455
Publikováno v:
Monatsh. Math.204 (2024), no.4, 969-987
We study the best coapproximation problem in Banach spaces, by using Birkhoff-James orthogonality techniques. We introduce two special types of subspaces, christened the anti-coproximinal subspaces and the strongly anti-coproximinal subspaces. We obt
Externí odkaz:
http://arxiv.org/abs/2407.14471
Publikováno v:
Aequationes Math. 97 (2023), no.1, 147-160
We study the James constant $J(\mathbb{X})$, an important geometric quantity associated with a normed space $ \mathbb{X} $, and explore its connection with isosceles orthogonality $ \perp_I. $ The James constant is defined as $J(\mathbb{X}) := \sup\{
Externí odkaz:
http://arxiv.org/abs/2407.14475
Publikováno v:
Linear Algebra and its applications 2021
We characterize Birkhoff-James orthogonality of continuous vector-valued functions on a compact topological space. As an application of our investigation, Birkhoff-James orthogonality of real bilinear forms are studied. This allows us to present an e
Externí odkaz:
http://arxiv.org/abs/2407.13713
Publikováno v:
Linear Algebra Appl. 690 (2024), 112-131
We investigate the local preservation of Birkhoff-James orthogonality at a point by a linear operator on a finite-dimensional Banach space and illustrate its importance in understanding the action of the operator in terms of the geometry of the conce
Externí odkaz:
http://arxiv.org/abs/2407.08900
Publikováno v:
J. Math. Anal. Appl. 494 (2021), no.1, Paper No. 124582, 22 pp
We study uniform $\epsilon-$BPB approximations of bounded linear operators between Banach spaces from a geometric perspective. We show that for sufficiently small positive values of $\epsilon,$ many geometric properties like smoothness, norm attainme
Externí odkaz:
http://arxiv.org/abs/2407.07490