Extremely amenable algebras

Anthony To-Ming Lau

Vol. 33 (1970), No. 2, 329–336

DOI: 10.2140/pjm.1970.33.329

Abstract

Let S be a semigroup and m(S) the space of bounded real functions on S. A subalgebra of m(,S) is extremely left amenable (ELA) if it is (sup) norm closed, left translation invariant, containing constants and has a multiplicative left invariant mean. S is ELA if m(S) is ELA. In this paper, we give a method in constructing all ELA subalgebras of m(S); it turns out that any such subalgebra of m(S) is contained in an ELA subalgebra which is the uniform limit of certain classes of simple functions on S.

Mathematical Subject Classification

Primary: 20.92

Milestones

Received: 20 June 1969

Published: 1 May 1970