Zobrazeno 1 - 10
of 393
pro vyhledávání: '"Paul, Kallol"'
Consider $\mathcal{H}$ is a complex Hilbert space and $A$ is a positive operator on $\mathcal{H}.$ The mapping $\langle\cdot,\cdot\rangle_A: \mathcal{H}\times \mathcal{H} \to \mathbb {C}$, defined as $\left\langle y,z\right\rangle_{A}=\left\langle Ay
Externí odkaz:
http://arxiv.org/abs/2407.21639
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 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
Publikováno v:
Colloq. Math.172 (2023), no.1, 65-83
We study extreme contractions in the setting of finite-dimensional polyhedral Banach spaces. Motivated by the famous Krein-Milman Theorem, we prove that a \emph{rank one} norm one linear operator between such spaces can be expressed as a convex combi
Externí odkaz:
http://arxiv.org/abs/2407.05545
Publikováno v:
Colloq. Math.172 (2023), no.2, 231-241
Let $\mathbb{X}$ be a Banach space and let $\mathbb{X}^*$ be the dual space of $\mathbb{X}.$ For $x,y \in \mathbb{X},$ $ x$ is said to be $T$-orthogonal to $y$ if $Tx(y) =0,$ where $T$ is a bounded linear operator from $\mathbb{X}$ to $\mathbb{X}^*.$
Externí odkaz:
http://arxiv.org/abs/2407.05541