An ergodic property of locally compact amenable semigroups

James Chin-Sze Wong

Vol. 48 (1973), No. 2, 615–619

DOI: 10.2140/pjm.1973.48.615

Abstract

Let M(S) be the Banach algebra of all bounded regular Borel measures on alocally compact semigroup S with variation norm and convolution as multiplication and M₀(S) the probability measures in M(S). We obtain necessary and sufficient conditions for the semigroup S to have the (ergodic) property that for each ν ∈ M(S),|ν(S)| = inf{∥ν ∗ μ∥ : μ ∈ M₀(S)}, an extension of a known result for locally compact groups.

Mathematical Subject Classification 2000

Primary: 43A07

Milestones

Received: 17 July 1972

Revised: 27 March 1973

Published: 1 October 1973