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, *) $ is a non-unital Banach algebra that possesses an approximate identity. Finally, it is shown that the Banach algebra $ M(G/H, *) $ is not involutive and also $ L^1(G/H, *) $ is a two-sided ideal of it.