Weakly Almost Periodic and Uniformly continuous functionals on the Orlicz Figa Talamanca Herz algebras

TL;DR

This paper investigates the properties of weakly almost periodic and uniformly continuous functionals on Orlicz Figa Talamanca Herz algebras, establishing the existence of a unique invariant mean and characterizing discrete groups.

Contribution

It introduces a unique invariant mean on weakly almost periodic functionals and characterizes discrete groups via functional inclusion relations.

Findings

Existence of a unique invariant mean on weakly almost periodic functionals.

Characterization of discrete groups through functional space inclusion.

Insights into the structure of Orlicz Figa Talamanca Herz algebras.

Abstract

In this paper we study weakly almost periodic and uniformly continuous functionals on the Orlicz Fig\`a-Talamanca Herz algebras associated to a locally compact group. We show that a unique invariant mean exists on the space of weakly almost periodic functionals. We also characterise discrete groups in terms of the inclusion of the space of uniformly continuous functions inside the space of weakly almost periodic functionals.