Isomorphism Theorems for the Algebras of $\Phi-$Pseudofunctions and $\Phi-$Pseudomeasures

TL;DR

This paper investigates when isometric algebra isomorphisms between $\

Contribution

It establishes isomorphism conditions for algebras of $\

Findings

Isometric isomorphisms imply topological group isomorphisms.

Provides an Orlicz space version of Parrott's theorem.

Advances understanding of algebraic structures related to $\

Abstract

In this article, we study the isomorphism problem for the algebras of $\Phi-$Pseudofunctions and $\Phi-$Pseudomeasures, denoted by $PF_\Phi(G)$ and $PM_\Phi(G),$ respectively. More precisely, for a certain class of Young functions $\Phi,$ we prove that if there exists an isometric isomorphism between $PF_\Phi(G_1)$ and $PF_\Phi(G_2),$ or between $PM_\Phi(G_1)$ and $PM_\Phi(G_2),$ then $G_1$ and $G_2$ are isomorphic as topological groups. In addition, we present an Orlicz version of Parrott's theorem.