A. Chattopadhyay

activity

20122025

most citedSecond order trace formulae

3 citations · 4 across the 24 of their papers we have counts for

collaborators

31 papers

math.FA2025

On modules of the Hardy space of Hartogs triangle

Arup Chattopadhyay, Saikat Giri, Shubham Jain

In this paper, we investigate the structure of doubly commuting submodules and quotient modules of the Hardy space $H^{2} (△_{H})$ over the Hartogs triangle. We establish a comp…

math.FA2024

Trace formulas for $S^{p}$ -perturbations and extension of Koplienko-Neidhardt trace formulas

Arup Chattopadhyay, Clément Coine, Saikat Giri +1

In this paper, we extend the class of admissible functions for the trace formula of the second order in the self-adjoint, unitary, and contraction cases for a perturbation in the H…

math.FA2024

Higher-Order Trace Formulas for Contractive and Dissipative Operators

Arup Chattopadhyay, Chandan Pradhan, Anna Skripka

We establish higher order trace formulas for pairs of contractions along a multiplicative path generated by a self-adjoint operator in a Schatten-von Neumann ideal, removing earlie…

math.FA2024

Differentiation, Taylor series, and all order spectral shift functions, for relatively bounded perturbations

Arup Chattopadhyay, Teun D. H. van Nuland, Chandan Pradhan

Given $H$ self-adjoint, $V$ symmetric and relatively $H$ -bounded, and $f : R \to C$ satisfying mild conditions, we show that the Gateaux derivative $$\frac{d^n}{dt^n}…

math.FA2024

Higher order $S^{p}$ -differentiability: The unitary case

Arup Chattopadhyay, Clément Coine, Saikat Giri +1

Consider the set of unitary operators on a complex separable Hilbert space $\hilh$, denoted as $\mathcal{U}(\hilh)$. Consider $1 < p < \infty$ . We establish that a function $f$ defined…

math.FA2023

Lipschitz Estimates and an application to trace formulae

Tirthankar Bhattacharyya, Arup Chattopadhyay, Saikat Giri +1

In this note, we provide an elementary proof for the expression of $f (U) - f (V)$ in the form of a double operator integral for every Lipschitz function $f$ on the unit circle $\cir$…

math.FA2023

Estimates and Higher-Order Spectral Shift Measures in Several Variables

Arup Chattopadhyay, Saikat Giri, Chandan Pradhan

In recent years, higher-order trace formulas of operator functions have attracted considerable attention to a large part of the perturbation theory community. In this direction, we…

math.FA2023

Trace formulas in higher dimensions

Arup Chattopadhyay, Saikat Giri, Chandan Pradhan +1

The paper establishes the Krein and Koplienko trace formulas for multivariable operator functions on symmetrically normed ideals of bounded operators. Results are proved for self-a…

math.FA2023

Schmidt subspaces of block Hankel operators

Arup Chattopadhyay, Soma Das, Chandan Pradhan

In scalar-valued Hardy space, the class of Schmidt subspaces for a bounded Hankel operator are closely related to nearly $S^{*}$ -invariant subspaces, as described by Gérard and Pushn…

math.FA2023

Approximation of the spectral action functional in the case of $τ$ -compact resolvents

Arup Chattopadhyay, Chandan Pradhan, Anna Skripka

We establish estimates and representations for the remainders of Taylor approximations of the spectral action functional $V \mapsto τ (f (H_{0} + V))$ on bounded self-adjoint perturbations…

math.FA2022

On Isometric Embeddability of $S_{q}^{m}$ into $S_{p}^{n}$ as non-commutative Quasi-Banach space

Arup Chattopadhyay, Guixiang Hong, Chandan Pradhan +1

The existence of isometric embedding of $S_{q}^{m}$ into $S_{p}^{n}$ , where $1 \leq p \neq = q \leq \infty$ and $m, n \geq 2$ has been recently studied in \cite{JFA22}. In this article, we extend…

math.FA2021

Commutants and Complex Symmetry of Finite Blaschke Product Multiplication Operator in $\bm{L^2(\T)}$

Arup Chattopadhyay, Soma Das

Consider the multiplication operator $M_{B}$ in $L^2(\T)$, where the symbol $B$ is a finite Blaschke product. In this article, we characterize the commutant of $M_{B}$ in $L^2(\T)$…

math.FA2021

Characterization of C-Symmetric Toeplitz operators for a Class of Conjugations in Hardy Spaces

Arup Chattopadhyay, Soma Das, Chandan Pradhan +1

In this article, we introduce a new class of conjugations in the scalar valued Hardy space $H_{C}^{2} (D)$ and provide a characterization of a complex symmetric Toep…

math.FA2021

Higher-order spectral shift for pairs of contractions via multiplicative path

Arup Chattopadhyay, Chandan Pradhan

In \cite{Mor}, Marcantognini and Morán obtained Koplienko-Neidhardt trace formula for pairs of contractions and pairs of maximal dissipative operators via multiplicative path. In t…

math.FA2021★ 3 cited

Second order trace formulae

Arup Chattopadhyay, Soma Das, Chandan Pradhan

Koplienko \cite{Ko} found a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class $B_{2} (H)$ . Later, Neidhardt introduce…

math.FA2021★ 1 cited

Trace formula for contractions and it's representation in $D$

Arup Chattopadhyay, Kalyan B. Sinha

The aim of this article is twofold: give a short proof of the existence of real spectral shift function and the associated trace formula for a pair of contractions, the difference…

math.FA2020

Koplienko-Neidhardt trace formula for unitaries $-$ A new proof

Arup Chattopadhyay, Soma Das, Chandan Pradhan

Koplienko \cite{Ko} found a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class $B_{2} (H)$ . Later in 1988, a similar f…

math.FA2020

Isometric Embeddability of $S_{q}^{m}$ into $S_{p}^{n}$

Arup Chattopadhyay, Guixiang Hong, Avijit Pal +2

In this paper, we study existence of isometric embedding of $S_{q}^{m}$ into $S_{p}^{n},$ where $1 \leq p \neq = q \leq \infty$ and $n \geq m \geq 2.$ We show that for all $n \geq m \geq 2$ if ther…

math.FA2020

Study of nearly invariant subspaces with finite defect in Hilbert spaces

Arup Chattopadhyay, Soma Das

In this article, we briefly describe nearly $T^{- 1}$ invariant subspaces with finite defect for a shift operator $T$ having finite multiplicity acting on a separable Hilbert space…

math.FA2020

Almost invariant subspaces of the shift operator on vector-valued Hardy spaces

Arup Chattopadhyay, Soma Das, Chandan Pradhan

In this article, we characterize nearly invariant subspaces of finite defect for the backward shift operator acting on the vector-valued Hardy space which is a vectorial generaliza…

math.FA2020

Kernels of Perturbed Toeplitz Operators in vector-valued Hardy spaces

Arup Chattopadhyay, Soma Das, Chandan Pradhan

Recently, Liang and Partington \cite{YP} show that kernels of finite-rank perturbations of Toeplitz operators are nearly invariant with finite defect under the backward shift opera…

math.FA2018

Multiplicities, invariant subspaces and an additive formula

Arup Chattopadhyay, Jaydeb Sarkar, Srijan Sarkar

Let $T = (T_{1}, \dots, T_{n})$ be a commuting tuple of bounded linear operators on a Hilbert space $H$ . The multiplicity of $T$ is the cardinality of a minimal generating s…

math.FA2017

Rank of a co-doubly commuting submodule is 2

Arup Chattopadhyay, B. Krishna Das, Jaydeb Sarkar

We prove that the rank of a non-trivial co-doubly commuting submodule is $2$ . More precisely, let $φ, ψ \in H^{\infty} (D)$ be two inner functions. If $\mathcal{Q}_φ = H^2(\ma…

math.FA2015

Helton-Howe-Carey-Pincus Trace Formula and Krein's Theorem

Arup Chattopadhyay, Kalyan B. Sinha

In this article, we derive the Helton-Howe-Carey-Pincus trace formula as a consequence of Krein's trace formula.

On modules of the Hardy space of Hartogs triangle

Trace formulas for Sp-perturbations and extension of Koplienko-Neidhardt trace formulas

Higher-Order Trace Formulas for Contractive and Dissipative Operators

Differentiation, Taylor series, and all order spectral shift functions, for relatively bounded perturbations

Higher order Sp-differentiability: The unitary case

Lipschitz Estimates and an application to trace formulae

Estimates and Higher-Order Spectral Shift Measures in Several Variables

Trace formulas in higher dimensions

Schmidt subspaces of block Hankel operators

Approximation of the spectral action functional in the case of τ-compact resolvents

On Isometric Embeddability of Sqm​ into Spn​ as non-commutative Quasi-Banach space

Commutants and Complex Symmetry of Finite Blaschke Product Multiplication Operator in $\bm{L^2(\T)}$

Characterization of C-Symmetric Toeplitz operators for a Class of Conjugations in Hardy Spaces

Higher-order spectral shift for pairs of contractions via multiplicative path

Second order trace formulae

Trace formula for contractions and it's representation in D

Koplienko-Neidhardt trace formula for unitaries − A new proof

Isometric Embeddability of Sqm​ into Spn​

Study of nearly invariant subspaces with finite defect in Hilbert spaces

Almost invariant subspaces of the shift operator on vector-valued Hardy spaces

Kernels of Perturbed Toeplitz Operators in vector-valued Hardy spaces

Multiplicities, invariant subspaces and an additive formula

Rank of a co-doubly commuting submodule is 2

Helton-Howe-Carey-Pincus Trace Formula and Krein's Theorem

Trace formulas for $S^{p}$ -perturbations and extension of Koplienko-Neidhardt trace formulas

Higher order $S^{p}$ -differentiability: The unitary case

Approximation of the spectral action functional in the case of $τ$ -compact resolvents

On Isometric Embeddability of $S_{q}^{m}$ into $S_{p}^{n}$ as non-commutative Quasi-Banach space

Trace formula for contractions and it's representation in $D$

Koplienko-Neidhardt trace formula for unitaries $-$ A new proof

Isometric Embeddability of $S_{q}^{m}$ into $S_{p}^{n}$