Soumitra Ghara

activity

20172026

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17 papers · 1 filter

math.FA2026

Inner multipliers, similarity and invariant subspaces for a class of Harmonically weighted Dirichlet spaces

Soumitra Ghara, Avipsa Patra

We consider the harmonically weighted Dirichlet spaces $D (μ)$ induced by Borel measures which are mutually absolutely continuous with respect to the Lebesgue measure $m$ on the uni…

math.FA2026

Circular operators and their strong circularity

Soumitra Ghara, Surjit Kumar, Shailesh Trivedi

Circular operators have been studied extensively since the work of R. Gellar, who conjectured that every circular operator on a complex separable Hilbert space is strongly circular…

math.FA2026

Unbounded Toeplitz operators and finite rank de Branges-Rovnyak spaces

Soumitra Ghara, MD Ramiz Reza, Chaman Kumar Sahu

Motivated by the recent developments of de Branges-Rovnyak spaces, we investigate the function theoretic aspects of finite rank de Branges-Rovnyak spaces $H (B)$ generated by row-va…

math.FA2025

Weakly $U (d)$ -homogeneous commuting tuple of bounded operators

Soumitra Ghara, Surjit Kumar, Shailesh Trivedi

We introduce and study the weakly $U (d)$ -homogeneous commuting tuple of operators. We provide a sufficient condition under which a weakly $U (d)$ -homogeneous tuple…

math.FA2024

A short note on similarity of operator-valued multishifts

Soumitra Ghara, Surjit Kumar, Shailesh Trivedi

A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This general…

math.FA2023

Cesàro summability of Taylor series in higher order weighted Dirichlet type spaces

Soumitra Ghara, Rajeev Gupta, Md. Ramiz Reza

For a positive integer $m$ and a finite non-negative Borel measure $μ$ on the unit circle, we study the Hadamard multipliers of higher order weighted Dirichlet-type spaces $\mathca…

math.FA2023

Dirichlet-type spaces of the bidisc and Toral $2$ -isometries

Santu Bera, Sameer Chavan, Soumitra Ghara

We introduce and study Dirichlet-type spaces $D (μ_{1}, μ_{2})$ of the unit bidisc $D^{2},$ where $μ_{1}, μ_{2}$ are finite positive Borel measures on the unit circle. We sho…

math.FA2023

Summability and duality

Soumitra Ghara, Javad Mashreghi, Thomas Ransford

We formalize the observation that the same summability methods converge in a Banach space $X$ and its dual $X^{*}$ . At the same time we determine conditions under which these methods…

math.FA2022

A local Douglas formula for higher order weighted Dirichlet-type integrals

Soumitra Ghara, Rajeev Gupta, Md. Ramiz Reza

We prove a local Douglas formula for higher order weighted Dirichlet-type integrals. With the help of this formula, we study the multiplier algebra of the associated higher order w…

math.FA2022

Analyticity, rank one perturbations and the invariance of the left spectrum

Sameer Chavan, Soumitra Ghara, Paramita Pramanick

We address the question of the analyticity of a rank one perturbation of an analytic operator. If $M_{z}$ is the bounded operator of multiplication by $z$ on a functional Hi…

math.FA2022

The relationship of the Gaussian curvature with the curvature of a Cowen-Douglas operator

Soumitra Ghara, Gadadhar Misra

It has been recently shown that if $K$ is a sesqui-analytic scalar valued non-negative definite kernel on a domain $Ω$ in $C^{m}$ , then the function $\big(K^2\partial_i\bar{\…

math.FA2022

Commuting Tuple of Multiplication Operators Homogeneous under the Unitary Group

Soumitra Ghara, Surjit Kumar, Gadadhar Misra +1

Let $U (d)$ be the group of $d \times d$ unitary matrices. We find conditions to ensure that a $U (d)$ -homogeneous $d$ -tuple $T$ is unitarily equivalent…

math.FA2021

The Cauchy dual subnormality problem via de Branges-Rovnyak spaces

Sameer Chavan, Soumitra Ghara, Md Ramiz Reza

The Cauchy dual subnormality problem (for short, CDSP) asks whether the Cauchy dual of a $2$ -isometry is subnormal. In this paper, we address this problem for cyclic $2$ -isometries…

math.FA2020

$K$ -homogeneous tuple of operators on bounded symmetric domains

Soumitra Ghara, Surjit Kumar, Paramita Pramanick

Let $Ω$ be an irreducible bounded symmetric domain of rank $r$ in $C^{d} .$ Let $K$ be the maximal compact subgroup of the identity component $G$ of the biholomorphic…

math.FA2019

Decomposition of the tensor product of two Hilbert modules

Soumitra Ghara, Gadadhar Misra

Given a pair of positive real numbers $α, β$ and a sesqui-analytic function $K$ on a bounded domain $Ω \subset C^{m}$ , in this paper, we investigate the properties of the sesq…

math.FA2018

The orbit of a bounded operator under the Möbius group modulo similarity equivalence

Soumitra Ghara

Let Möb denote the group of biholomorphic automorphisms of the unit disc and $(\mbox{Möb} \cdot T)$ be the orbit of a Hilbert space operator $T$ under the action of Möb. If the quo…

math.FA2017

On sum of two subnormal kernels

Soumitra Ghara, Surjit Kumar

We show, by means of a class of examples, that if $K_{1}$ and $K_{2}$ are two positive definite kernels on the unit disc such that the multiplication by the coordinate function on the…

Inner multipliers, similarity and invariant subspaces for a class of Harmonically weighted Dirichlet spaces

Circular operators and their strong circularity

Unbounded Toeplitz operators and finite rank de Branges-Rovnyak spaces

Weakly U(d)-homogeneous commuting tuple of bounded operators

A short note on similarity of operator-valued multishifts

Cesàro summability of Taylor series in higher order weighted Dirichlet type spaces

Dirichlet-type spaces of the bidisc and Toral 2-isometries

Summability and duality

A local Douglas formula for higher order weighted Dirichlet-type integrals

Analyticity, rank one perturbations and the invariance of the left spectrum

The relationship of the Gaussian curvature with the curvature of a Cowen-Douglas operator

Commuting Tuple of Multiplication Operators Homogeneous under the Unitary Group

The Cauchy dual subnormality problem via de Branges-Rovnyak spaces

K-homogeneous tuple of operators on bounded symmetric domains

Decomposition of the tensor product of two Hilbert modules

The orbit of a bounded operator under the Möbius group modulo similarity equivalence

On sum of two subnormal kernels

Weakly $U (d)$ -homogeneous commuting tuple of bounded operators

Dirichlet-type spaces of the bidisc and Toral $2$ -isometries

$K$ -homogeneous tuple of operators on bounded symmetric domains