  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 $M(G/H)$.
