Document Type

Article

Publication Date

2008

Publication Title

Mathematical Proceedings of the Cambridge Philosophical Society

Volume

144

First Page

697

Last Page

706

DOI

10.1017/S0305004108001126

Abstract

We introduce the notion of character amenable Banach algebras. We prove that character amenability for either of the group algebra L(1)(G) or the Fourier algebra A(G) is equivalent to the amenability of the underlying group G. Character amenability of the measure algebra M(G) is shown to be equivalent to G being a discrete amenable group. We also study functorial properties of character amenability. For a commutative character amenable Banach algebra A, we prove all cohomological groups with coefficients in finite-dimensional Banach A-bimodules, vanish. As a corollary we conclude that all finite-dimensional extensions of commutative character amenable Banach algebras split strongly.

Comments

This article was first publishing in the Mathematical Proceedings of the Cambridge Philosophical Society, 2008. It is available here. Copyright (2012) Cambridge University Press.

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