Vol. 33, No. 2, 1970

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Extremely amenable algebras

Anthony To-Ming Lau

Vol. 33 (1970), No. 2, 329–336

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
Received: 20 June 1969
Published: 1 May 1970
Anthony To-Ming Lau