Banach Algebra of Complex Bounded Radon Measures on Homogeneous Space

Abstract

Let $H$ be a compact subgroup of a locally compact group $G$. In this paper we define a convolution on $M(G/H)$, the space of all complex bounded Radon measures on the homogeneous space G/H. Then we prove that the measure space $M(G/H,\ast )$ is a non-unital Banach algebra that possesses an approximate identity. Finally, it is shown that the Banach algebra $M(G/H,\ast )$ is not involutive and also $L^1(G/H,\ast )$ is a two-sided ideal of it.