arXiv subjects

C. R. Jayanarayanan

Publications and source records attributed to C. R. Jayanarayanan.

3 recordsLinked to original sources

arXiv2026

Connections between Essential Norm, Bhatia-Šemrl Property and Strong Subdifferentiability of Operators on Banach Spaces

We study Birkhoff-James orthogonality in spaces of bounded linear operators between Banach spaces through the Bhatia-Šemrl property. We investigate the interplay among three key properties of bounded linear operators: strong subdifferentiability, the Bhatia-Šemrl property, and the condition that the essential norm is strictly less than the operator norm. For a Hilbert space $H$ and for $1<p,q<\infty$, we show that for any nonzero operator in $B(H)$ and $B(\ell^p, \ell^q)$, the essential norm is strictly less than the operator norm if and only if it is a point of strong subdifferentiability of the norm and its norm-attainment set is compact. Moreover, for nonzero operators in these spaces that satisfy the Bhatia-Šemrl property, we show that their essential norm must be strictly less than their operator norm. We also study norm one projections satisfying the Bhatia-Šemrl property and provide examples of operators that possess this property.

math.FA↗

arXiv2020

Structure of sets of strong subdifferentiability in dual $L^1$-spaces

In this article, we analyse the structure of finite dimensional subspaces of the set of points of strong subdifferentiability in a dual space. In a dual $L_1(μ)$ space, such a subspace is in the discrete part of the Yoshida-Hewitt type decomposition. In this set up, any Banach space consisting of points of strong subdifferentiability is necessarily finite dimensional. Our results also lead to streamlined and new proofs of results from the study of strong proximinality for subspaces of finite co-dimension in a Banach space.

math.FA↗

arXiv2020

Ball proximinality of $M$-ideals of compact operators

In this article, we prove the proximinality of closed unit ball of $M$-ideals of compact operators. We also prove the ball proximinality of $M$-embedded spaces in their biduals. Moreover, we show that $\mathcal{K}(\ell_1)$, the space of compact operators on $\ell_1$, is ball proximinal in $\mathcal{B}(\ell_1)$, the space of bounded operators on $\ell_1$, even though $\mathcal{K}(\ell_1)$ is not an $M$-ideal in $\mathcal{B}(\ell_1)$.

math.FA↗