Sourav Pal

activity

20172026

most citedCharacterizations and models for the

C_{1, r}

class and quantum annulus

1 citations · 2 across the 23 of their papers we have counts for

collaborators

25 papers

math.FA2026

Spectral constants for the quantum annulus

Sourav Pal, James E. Pascoe, Nitin Tomar

We find several new estimates for the spectral constants $K (A_{r})$ for which a closed annulus $A_{r}$ or closed polyannulus $A_{r}^{n}$ is a…

math.FA2025

Constrained dilation and $Γ$ -contractions

Sourav Pal, Nitin Tomar

A commuting pair of Hilbert space operators having the closed symmetrized bidisc \[ Γ=\{(z_1+z_2, z_1z_2) \in \mathbb C^2 \ : \ |z_1| \leq 1, |z_2| \leq 1\} \] as a spectral set is…

math.FA2025

Operators associated with a domain in $C^{4}$ and applications

Sourav Pal, Nitin Tomar

The hexablock is a domain arising from a special case of the $μ$ -synthesis problem. We study the commuting operator tuples having the hexablock as a spectral set. Such a tuple is c…

math.CV2025

The Hexablock: a domain associated with the $μ$ -synthesis in $M_{2} (C)$

Indranil Biswas, Sourav Pal, Nitin Tomar

We introduce a domain named \textit{hexablock} in $C^{4}$ and show that its origin is a special case of $μ$ -synthesis in $M_{2} (C)$ , more precisely the $μ_{E}$ -unit ball…

math.FA2025

Dilation on an annulus and von Neumann's inequality on certain varieties in the biball

Sourav Pal, Nitin Tomar

We give an alternative proof to Agler's famous result on success of rational dilation on an annulus by an application of a result due to Dritschel and McCullough. We show interplay…

math.FA2024

Spectral set, complete spectral set and dilation for Banach space operators

Swapan Jana, Sourav Pal

Famous results due to von Neumann, Sz.-Nagy and Arveson assert that the following four statements are equivalent; a Hilbert space operator $T$ is a contraction; the closed unit dis…

math.FA2024

Classification and dilation for $q$ -commuting $2 \times 2$ scalar matrices

Sourav Pal, Prajakta Sahasrabuddhe, Nitin Tomar

A tuple $T = (T_{1}, \dots, T_{k})$ of operators on a Hilbert space $H$ is said to be \textit{ $q$ -commuting with} $∥ q ∥ = 1$ or simply $q$ -\textit{commuting} if ther…

math.FA2024

Theory of $q$ -commuting contractions-II: Regular dilation, Brehmer's positivity and von Neumann's inequality

Sourav Pal, Prajakta Sahasrabuddhe, Nitin Tomar

It is well-known that a commuting family of contractions possesses a regular unitary dilation if and only if it satisfies Brehmer's positivity condition. We extend this theorem to…

math.FA2024

A dilation theoretic approach to Banach spaces

Swapan Jana, Sourav Pal, Saikat Roy

For a complex Banach space $X$ , we prove that $X$ is a Hilbert space if and only if every strict contraction $T$ on $X$ dilates to an isometry if and only i…

math.FA2024

Remarks on positive definite functions on a group

Swapan Jana, Sourav Pal, Nitin Tomar

We study the operator-valued positive definite functions on a group using positive block matrices. We give an alternative proof to Brehmer positivity for doubly commuting contracti…

math.FA2023

Joint reducing subspaces and orthogonal decompositions of operators in an annulus

Sourav Pal, Nitin Tomar

A commuting tuple of Hilbert space operators $(T_{1}, \dots, T_{n})$ is said to be an \textit{ $A_{r}^{n}$ -contraction} if the closure of the polyannulus \[ \mathbb A_r^n=\left\{(…

math.FA2023

The $2 \times 2$ block matrices associated with an annulus

Sourav Pal, Nitin Tomar

A bounded Hilbert space operator $T$ for which the closure of the annulus \[ \mathbb{A}_r=\{z \ : \ r<|z|<1\} \subseteq \mathbb{C}, \qquad (0<r<1) \] is a spectral set is called an…

math.FA2023

Operators associated with the pentablock and their relations with biball and symmetrized bidisc

Sourav Pal, Nitin Tomar

A commuting triple of Hilbert space operators $(A, S, P)$ is said to be a \textit{ $P$ -contraction} if the closed pentablock $P$ is a spectral set for $(A,…

math.FA2023

Dilation and Birkhoff-James orthogonality

Sourav Pal, Saikat Roy

We study the interaction between unitary $ρ$ -dilations of a pair of Hilbert space operators and Birkhoff-James orthogonality. We prove that for two orthogonal operators $T, A$ if $\…

math.FA2023

Dilation of normal operators associated with an annulus

Sourav Pal, Nitin Tomar

For $0 < r < 1$ , let us consider the following annulus: \[ \mathbb A_r= \{ z\in \mathbb C\, : \, r<|z|<1 \}. \] A Hilbert space operator $T$ for which $A_{r}$ is a spe…

math.FA2022

Theory of q-commuting contractions : joint reducing subspaces and orthogonal decompositions

Sourav Pal, Prajakta Sahasrabuddhe, Nitin Tomar

In the literature, we have several results associated with canonical decomposition of commuting contractions. In this paper, we generalize a few of these results to $Q$ -commuting c…

math.FA2022

Lifting $Q$ -commuting and $Q$ -intertwining operators

Sourav Pal, Prajakta Sahasrabuddhe

There are several proofs of the classical commutant lifting and intertwining lifting theorems in the literature. In this article, we present analogous proofs to a few $Q$ -commuting…

math.FA2022★ 1 cited

Characterizations and models for the $C_{1, r}$ class and quantum annulus

Sourav Pal, Nitin Tomar

For fixed $0 < r < 1$ , let $A_{r} = {z \in C : r < ∣ z ∣ < 1}$ be the annulus with boundary $\partial A_{r} = T \cup r T$ , where $T$ is the unit circle…

math.FA2022

Triangular Tetrablock-contractions, factorization of contractions, dilation and subvarieties

Sourav Pal

A commuting triple of Hilbert space operators $(A, B, P)$ , for which the closed tetrablock $E ˉ$ is a spectral set, is called a \textit{tetrablock-contraction} or simply…

math.FA2022

Minimal unitary dilations for commuting contractions

Sourav Pal, Prajakta Sahasrabuddhe

For commuting contractions $T_{1}, \dots, T_{n}$ acting on a Hilbert space $H$ with $T = \prod_{i = 1}^{n} T_{i}$ , we show that $(T_{1}, \dots, T_{n})$ dilates to commuting isometries $(V_…

math.AG2022

Distinguished varieties in the polydisc and dilation of commuting contractions

Sourav Pal

A distinguished variety in the polydisc $D^{n}$ is an affine complex algebraic variety that intersects $D^{n}$ and exits the domain through the $n$ -torus $T^{n}$ …

math.FA2022

The toral contractions and $Γ$ -distinguished $Γ$ -contractions

Sourav Pal, Nitin Tomar

A pair of commuting Hilbert space contractions $(T_{1}, T_{2})$ is said to be toral if there is a polynomial $p \in C [z_{1}, z_{2}]$ such that its zero set $Z (p)$ defines a distingui…

math.FA2022

Common reducing subspaces and decompositions of contractions

Sourav Pal

A commuting triple of Hilbert space operators $(A, B, P)$ , for which the closed tetrablock $E$ is a spectral set, is called a \textit{tetrablock-contraction} or si…

math.FA2020

Distinguished varieties in a family of domains associated with spectral interpolation and operator theory

Sourav Pal

We find characterization for the distinguished varieties in the symmetrized polydisc $G_{n} (n \geq 2)$ and thus generalize the work [\textit{J. Funct. Anal.}, 266 (2014),…

Spectral constants for the quantum annulus

Constrained dilation and Γ-contractions

Operators associated with a domain in C4 and applications

The Hexablock: a domain associated with the μ-synthesis in M2​(C)

Dilation on an annulus and von Neumann's inequality on certain varieties in the biball

Spectral set, complete spectral set and dilation for Banach space operators

Classification and dilation for q-commuting 2×2 scalar matrices

Theory of q-commuting contractions-II: Regular dilation, Brehmer's positivity and von Neumann's inequality

A dilation theoretic approach to Banach spaces

Remarks on positive definite functions on a group

Joint reducing subspaces and orthogonal decompositions of operators in an annulus

The 2×2 block matrices associated with an annulus

Operators associated with the pentablock and their relations with biball and symmetrized bidisc

Dilation and Birkhoff-James orthogonality

Dilation of normal operators associated with an annulus

Theory of q-commuting contractions : joint reducing subspaces and orthogonal decompositions

Lifting Q-commuting and Q-intertwining operators

Characterizations and models for the C1,r​ class and quantum annulus

Triangular Tetrablock-contractions, factorization of contractions, dilation and subvarieties

Minimal unitary dilations for commuting contractions

Distinguished varieties in the polydisc and dilation of commuting contractions

The toral contractions and Γ-distinguished Γ-contractions

Common reducing subspaces and decompositions of contractions

Distinguished varieties in a family of domains associated with spectral interpolation and operator theory

Constrained dilation and $Γ$ -contractions

Operators associated with a domain in $C^{4}$ and applications

The Hexablock: a domain associated with the $μ$ -synthesis in $M_{2} (C)$

Classification and dilation for $q$ -commuting $2 \times 2$ scalar matrices

Theory of $q$ -commuting contractions-II: Regular dilation, Brehmer's positivity and von Neumann's inequality

The $2 \times 2$ block matrices associated with an annulus

Lifting $Q$ -commuting and $Q$ -intertwining operators

Characterizations and models for the $C_{1, r}$ class and quantum annulus

The toral contractions and $Γ$ -distinguished $Γ$ -contractions