Abstract Structure of Measure Algebras on Coset Spaces of Compact Subgroups in Locally Compact Groups

Abstract

This paper presents a systematic operator theory approach for abstract structure of Banach measure algebras over coset spaces of compact subgroups. Let H be a compact subgroup of a locally compact group G and G/H be the left coset space associated to the subgroup H in G. Also, let M (G/H) be the Banach measure space consists of all complex measures over G/H. We then introduce an operator theoretic characterization for the abstract notion of involution over the Banach measure space M (G/H).