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

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