Isomorphism Theorems for the Algebras of $Φ-$Pseudofunctions and $Φ-$Pseudomeasures

Fuente: arXiv
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Main Authors: Dabra, Arvish, Kumar, N. Shravan
Format: Preprint
Published: 2025
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author Dabra, Arvish
Kumar, N. Shravan
author_facet Dabra, Arvish
Kumar, N. Shravan
contents In this article, we study the isomorphism problem for the algebras of $Φ-$Pseudofunctions and $Φ-$Pseudomeasures, denoted by $PF_Φ(G)$ and $PM_Φ(G),$ respectively. More precisely, for a certain class of Young functions $Φ,$ we prove that if there exists an isometric isomorphism between $PF_Φ(G_1)$ and $PF_Φ(G_2),$ or between $PM_Φ(G_1)$ and $PM_Φ(G_2),$ then $G_1$ and $G_2$ are isomorphic as topological groups. In addition, we present an Orlicz version of Parrott's theorem.
format Preprint
id arxiv_https___arxiv_org_abs_2507_13020
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Isomorphism Theorems for the Algebras of $Φ-$Pseudofunctions and $Φ-$Pseudomeasures
Dabra, Arvish
Kumar, N. Shravan
Functional Analysis
Primary 46E30, 43A22, Secondary 43A15
In this article, we study the isomorphism problem for the algebras of $Φ-$Pseudofunctions and $Φ-$Pseudomeasures, denoted by $PF_Φ(G)$ and $PM_Φ(G),$ respectively. More precisely, for a certain class of Young functions $Φ,$ we prove that if there exists an isometric isomorphism between $PF_Φ(G_1)$ and $PF_Φ(G_2),$ or between $PM_Φ(G_1)$ and $PM_Φ(G_2),$ then $G_1$ and $G_2$ are isomorphic as topological groups. In addition, we present an Orlicz version of Parrott's theorem.
title Isomorphism Theorems for the Algebras of $Φ-$Pseudofunctions and $Φ-$Pseudomeasures
topic Functional Analysis
Primary 46E30, 43A22, Secondary 43A15
url https://arxiv.org/abs/2507.13020