# Abstract structure of Banach function algebras on homogeneous spaces of compact groups

#### Dr Arash Ghaani Farashahi, University of Leeds. Part of the Analysis and Applications Seminar Series.

I will discuss abstract structure of classical Banach function *-algebras on homogeneous spaces (coset spaces) of compact groups. Suppose $G$ is a compact group and $H$ is a closed subgroup of $G$. Let $G/H$ be the left coset space of $H$ in $G$ and $\mu$ be the $G$-invariant measure on the homogeneous space $G/H$ normalized with respect to Weil's formula. I shall talk about the abstract notions of convolution and involution for functions in $L^p(G/H,\mu)$, for all $p\ge 1$.