Vol. 48, No. 2, 1973

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An ergodic property of locally compact amenable semigroups

James Chin-Sze Wong

Vol. 48 (1973), No. 2, 615–619
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
Authors
James Chin-Sze Wong