Virtual diagonals and n-amenability for Banach algebras

Alan L. T. Paterson

Vol. 175 (1996), No. 1, 161–185

DOI: 10.2140/pjm.1996.175.161

Abstract

We develop higher dimensional amenability for Banach algebras from the viewpoint of Banach homology theory. In particular, we show that such amenability is equivalent to the flatness of a certain bimodule and a resultant splitting module map gives rise to the higher dimensional virtual diagonals of Effros and Kishimoto. The theory is developed for the non-unital case. Examples of n-amenability are given and it is shown (among other results) that a 2-amenable Banach algebra is amenable if and only if there exists an inner 2-virtual diagonal.

Mathematical Subject Classification 2000

Primary: 46M20

Secondary: 46H05

Milestones

Received: 17 January 1994

Revised: 1 February 1995

Published: 1 September 1996