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Character Amenability of Lipschitz Algebras

Published online by Cambridge University Press:  20 November 2018

Mahshid Dashti ,
Rasoul Nasr-Isfahani  and
Sima Soltani Renani
Mahshid Dashti
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran e-mail: m.dashti@math.iut.ac.irisfahani@cc.iut.ac.irsimasoltani@cc.iut.ac.ir
Rasoul Nasr-Isfahani
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran e-mail: m.dashti@math.iut.ac.irisfahani@cc.iut.ac.irsimasoltani@cc.iut.ac.ir
Sima Soltani Renani
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran e-mail: m.dashti@math.iut.ac.irisfahani@cc.iut.ac.irsimasoltani@cc.iut.ac.ir
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Abstract

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Let $\chi $ be a locally compact metric space and let $\mathcal{A}$ be any of the Lipschitz algebras $\text{Li}{{\text{p}}_{\alpha }}\text{ }\!\!\chi\!\!\text{ }$, $\text{Li}{{\text{p}}_{\alpha }}\text{ }\!\!\chi\!\!\text{ }$, or $\text{lip}_{\alpha }^{0}\,\chi $. 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 $\chi $ is uniformly discrete.

Keywords

43A0746H0546J10character amenablecharacter contractibleLipschitz algebrasspectrum
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 37 - 41
Copyright
Copyright © Canadian Mathematical Society 2014

References

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