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.

Abstract Structure of Measure Algebras on Coset Spaces of Compact Subgroups in Locally Compact Groups

“…Remark 5.3. The convolution given by (5.1) introduced in Theorem 2.9 of [1] and studied with different notions in some directions.…”