Banach Algebra of Bounded Complex 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 bounded complex Radon measures on the homogeneous space G/H. Then we prove that the measure space M(G/H) with the newly well-defined convolution is a non-unital Banach algebra that possesses an approximate identity. Finally, it is shown that this Banach algebra is not involutive and also L1(G/ H) with the new convolution is a two-sided ideal of it.