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

Abstract

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

13 Pages