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Character amenability of Banach algebras

Published online by Cambridge University Press:  01 May 2008

MEHDI SANGANI MONFARED
MEHDI SANGANI MONFARED*
Affiliation:
Department of Mathematics and Statistics, University of Windsor, Windsor, ON, N9B 3P4, Canada. e-mail: [email protected]
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Abstract

We introduce the notion of character amenable Banach algebras. We prove that character amenability for either of the group algebra L1(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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 3 , May 2008 , pp. 697 - 706
Copyright
Copyright © Cambridge Philosophical Society 2008

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