On the convolution algebras of H-invariant measures

John Yuan

Vol. 62 (1976), No. 2, 595–600

DOI: 10.2140/pjm.1976.62.595

Abstract

The totality M(eSe∕H) of bounded regular Borel measures on the orbit space eSe∕H, where S is a locally compact semigroup and H is a compact subgroup with the identity e, forms a Banach space; however, its closed subspace M_H(ESe∕H) of H-invariant measures forms even a Banach algebra under a suitable convolution. Furthermore, if w is an idempotent probability measure with compact support on S, then w ∗ M(S) ∗ w≅w_H ∗ M(S) ∗ w_H≅NI_H(eSe∕H) algebraically and in various topologies, where w_H is the normalized Haar measure on some compact subgroup H.

Mathematical Subject Classification 2000

Primary: 43A10

Milestones

Received: 12 May 1975

Revised: 7 October 1975

Published: 1 February 1976