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

## TL;DR

This paper develops an operator theory framework to understand the structure of Banach measure algebras on coset spaces of compact subgroups within locally compact groups, focusing on involution properties.

## Contribution

It introduces an operator theoretic characterization of involution in Banach measure algebras on coset spaces, advancing the abstract understanding of these algebraic structures.

## Key findings

- Operator theoretic characterization of involution
- Structural insights into Banach measure algebras
- Framework applicable to coset spaces of compact subgroups

## 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 $M(G/H)$.