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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 character amenable, character contractible, Lipschitz algebras, spectrum
MSC Classifications: 43A07, 46H05, 46J10 show english descriptions Means on groups, semigroups, etc.; amenable groups
General theory of topological algebras
Banach algebras of continuous functions, function algebras [See also 46E25]
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]
 

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