Characterizations of amenable and strongly amenable C^∗-algebras

John Winston Bunce

Vol. 43 (1972), No. 3, 563–572

DOI: 10.2140/pjm.1972.43.563

Abstract

In this paper it is proved that a C^∗-algebra A is strongly amenable iff A satisfies a certain fixed point property when acting on a compact convex set, or iff a certain Hahn-Banach type extension theorem is true for all Banach A-modules. It is proved that a C^∗-algebra A is amenable iff A satisfies a weaker Hahn-Banach type extension theorem.

Mathematical Subject Classification 2000

Primary: 46L05

Milestones

Received: 27 September 1971

Published: 1 December 1972