P. Dabhi

activity

20222026

collaborators

10 papers

math.FA2026

The BSE Property for Weighted Banach Algebras of Dirichlet Series

Prakash A. Dabhi

Let $ω : N \to [1, \infty)$ be a weight on the multiplicative semigroup of natural numbers. We investigate the Bochner-Schoenberg-Eberlein (BSE) property for the weighted B…

math.FA2026

On Multiplicity of Uniform Norms and Maximal Spectral Substructures in Commutative Banach Algebras

Jekwin J. Dabhi, Prakash A. Dabhi

Let $A$ be a semisimple commutative Banach algebra. It is shown that either $A$ has exactly one uniform norm or it admits uncountably many uniform norms. Further,…

math.FA2026

On the BSE- property of vector valued Beurling algebra $L^{1} (G, ω, A)$

Jekwin Dabhi, Prakash Dabhi

Let $G$ be a locally compact abelian group, and let $ω : G \to [1, \infty)$ be a measurable weight, i.e., $ω$ is measurable, and $ω (s + t) \leq ω (s) ω (t)$ for all $s, t \in G$ . Let $\math…

math.FA2026

Wiener type theorems for countable limits of quasi-Beurling algebras and maximizing results on weights

Prakash A. Dabhi, Karishman B. Solanki

We establish the vector-valued Wiener type theorems for countable projective and inductive limits of quasi-Banach algebras in a weighted setting for both finite and infinite dimens…

math.FA2026

On the BSE and BED properties of the Beurling algebra $L^{1} (G, ω)$

Jekwin J. Dabhi, Prakash A. Dabhi

Let $G$ be a locally compact abelian group, and let $ω : G \to [1, \infty)$ be a weight, i.e., $ω$ is measurable, $ω$ is locally bounded and $ω (s + t) \leq ω (s) ω (t)$ for all $s, t \in G$ …

math.FA2025

Weighted inversion of vector valued Dirichlet series

Prakash A. Dabhi, Karishman B. Solanki

Let $Λ \subset [0, \infty)$ be an additive semigroup with $0 \in Λ$ , $ω$ be an admissible weight on $Λ$ , $A$ be a unital Banach algebra, and let $f (s) = \sum_{λ \in Λ} f_{λ} e^{- λ s}$ …

math.FA2025

Inverse-closedness of weighted Schur and BGS type quasi-Banach algebras

Prakash A. Dabhi, Karishman B. Solanki

We prove that the weighted quasi-Banach algebras of operator valued matrices satisfying Schur and Baskakov-Gohberg-Sjöstrand (BGS) conditions are inverse-closed in the Banach algeb…

math.FA2024

On inversion of absolutely convergent weighted Dirichlet series in two variables

Prakash A. Dabhi

Let $0 < p \leq 1$ , and let $ω : N^{2} \to [1, \infty)$ be an almost monotone weight. Let $H$ be the closed right half plane in the complex plane. Let $a$ be a c…

math.FA2022

Vector valued Beurling algebra analogues of Wiener's Theorem

Prakash A. Dabhi, Karishman B. Solanki

Let $0 < p \leq 1$ , $ω$ be a weight on $Z$ , and let $A$ be a unital Banach algebra. If $f$ is a continuous function from the unit circle $T$ to $A$ s…

math.FA2022

Symmetry and inverse-closedness of some $p$ -Beurling algebras

Prakash A. Dabhi, Karishman B. Solanki

Let $(G, d)$ be a metric space with the counting measure $μ$ satisfying some growth conditions. Let $ω (x, y) = (1 + d (x, y))^{δ}$ for some $0 < δ \leq 1$ . Let $0 < p \leq 1$ . Let $A_{p ω}$ …

The BSE Property for Weighted Banach Algebras of Dirichlet Series

On Multiplicity of Uniform Norms and Maximal Spectral Substructures in Commutative Banach Algebras

On the BSE- property of vector valued Beurling algebra L1(G,ω,A)

Wiener type theorems for countable limits of quasi-Beurling algebras and maximizing results on weights

On the BSE and BED properties of the Beurling algebra L1(G,ω)

Weighted inversion of vector valued Dirichlet series

Inverse-closedness of weighted Schur and BGS type quasi-Banach algebras

On inversion of absolutely convergent weighted Dirichlet series in two variables

Vector valued Beurling algebra analogues of Wiener's Theorem

Symmetry and inverse-closedness of some p-Beurling algebras

On the BSE- property of vector valued Beurling algebra $L^{1} (G, ω, A)$

On the BSE and BED properties of the Beurling algebra $L^{1} (G, ω)$

Symmetry and inverse-closedness of some $p$ -Beurling algebras