Kousik Dhara

activity

20202024

collaborators

7 papers

math.FA2024

Toeplitz, Hankel, de Branges and two truncated matrix moment problems

Kousik Dhara, Harry Dym

This paper deals with (1) the truncated matrix Hamburger moment problem from the point of view of reproducing kernel Hilbert spaces of vector valued entire functions of the kind in…

math.FA2024

The Bishop-Phelps-Bollobas property for certain Banach spaces

Tirthankar Bhattacharyya, Mainak Bhowmik, Kousik Dhara

Let $X$ be a complex Banach space. We prove that if $L$ is an extremally disconnected compact Hausdorff topological space, then the pair $(X, C (L))$ satisfies the Bishop-Phelps-Bol…

math.FA2022

Pseudo $S$ -spectra of special operators in quaternionic Hilbert spaces

Kousik Dhara, Santhosh Kumar Pamula

For a bounded quaternionic operator $T$ on a right quaternionic Hilbert space $H$ and $ε > 0$ , the pseudo $S$ -spectrum of $T$ is defined as \begin{align*} Λ_{\va…

math.FA2022

Norms of basic operators in vector valued model spaces and de Branges spaces

Kousik Dhara, Harry Dym

Let $Ω_{+}$ be either the open unit disc or the open upper half plane or the open right half plane. In this paper, we compute the norm of the basic operator $A_α=Π_ΘT_{b_α}|_{\mathca…

math.FA2021

A Bishop-Phelps-Bollobás theorem for bounded analytic functions

Neeru Bala, Kousik Dhara, Jaydeb Sarkar +1

Let $H^{\infty}$ denote the Banach algebra of all bounded analytic functions on the open unit disc and denote by $B (H^{\infty})$ the Banach space of all bounded linear operat…

math.FA2021

Idempotent, model, and Toeplitz operators attaining their norms

Neeru Bala, Kousik Dhara, Jaydeb Sarkar +1

We study idempotent, model, and Toeplitz operators that attain the norm. Notably, we prove that if $Q$ is a backward shift invariant subspace of the Hardy space $H^2(\mat…

math.FA2020

Orthogonality in Banach Spaces via projective tensor product

Kousik Dhara, Narayan Rakshit, Jaydeb Sarkar +1

Let $X$ be a complex Banach space and $x, y \in X$ . By definition, we say that $x$ is Birkhoff-James orthogonal to $y$ if $∥ x + λ y ∥_{X} \geq ∥ x ∥_{X}$ for all $λ \in C$ . We…