A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups

This paper introduces a class of abstract linear representations on Banach convolution function algebras over homogeneous spaces of compact groups. Let G be a compact group and H a closed subgroup of G . Let μ be the normalized G -invariant measure over the compact homogeneous space G/H associated with Weil's formula and 1≤p<∞ . We then present a structured class of abstract linear representations of the Banach convolution function algebras Lp(G/H,μ).