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# Character Amenability of Lipschitz Algebras

Published:2012-07-16
Printed: Mar 2014
• Mahshid Dashti,
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran
• Rasoul Nasr-Isfahani,
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran
• Sima Soltani Renani,
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran
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## Abstract

Let ${\mathcal X}$ be a locally compact metric space and let ${\mathcal A}$ be any of the Lipschitz algebras ${\operatorname{Lip}_{\alpha}{\mathcal X}}$, ${\operatorname{lip}_{\alpha}{\mathcal X}}$ or ${\operatorname{lip}_{\alpha}^0{\mathcal X}}$. In this paper, we show, as a consequence of rather more general results on Banach algebras, that ${\mathcal A}$ is $C$-character amenable if and only if ${\mathcal X}$ is uniformly discrete.
 Keywords: character amenable, character contractible, Lipschitz algebras, spectrum
 MSC Classifications: 43A07 - Means on groups, semigroups, etc.; amenable groups 46H05 - General theory of topological algebras 46J10 - Banach algebras of continuous functions, function algebras [See also 46E25]