Document Type
Article
Publication Date
2008
Publication Title
Mathematical Proceedings of the Cambridge Philosophical Society
Volume
144
First Page
697
Last Page
706
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.
DOI
10.1017/S0305004108001126
Recommended Citation
Monfared, Mehdi S.. (2008). Character amenability of Banach algebras. Mathematical Proceedings of the Cambridge Philosophical Society, 144, 697-706.
https://scholar.uwindsor.ca/mathstatspub/3
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.