Orlicz Algebras on Homogeneous Spaces of Compact Groups and Their Abstract Linear Representations

Abstract

Let G be a compact group, H a closed subgroup of G and let m be the normalized G-invariant measure on the homogeneous space G / H obtained from Weil’s formula. In this article, for a given Young function $$\varphi $$ , we give a new class of Banach convolution algebras on homogeneous spaces of compact groups by introducing a convolution and an involution on the Orlicz space $$L^\varphi (G/H, m)$$ . Finally, a class of linear representations of this class of Banach convolution algebras is presented.