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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the $ C\sp \ast$-algebra generated by the left regular representation of a locally compact group


Author: Erik Bédos
Journal: Proc. Amer. Math. Soc. 120 (1994), 603-608
MSC: Primary 22D25; Secondary 43A07, 46L05
MathSciNet review: 1181157
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Abstract: Let $ \lambda $ denote the left regular representation of a locally compact group $ G$ on $ {L^2}(G)$ and $ {C^{\ast}}(\lambda (G))$ the $ {C^{\ast}}$-algebra generated by $ \lambda (G)$. We show that the amenability of $ G$ and the amenability of $ G$ considered as a discrete group both may be characterized in terms of $ {C^{\ast}}(\lambda (G))$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1181157-1
PII: S 0002-9939(1994)1181157-1
Keywords: $ {C^{\ast}}$-algebra, regular representation, amenability, nuclearity
Article copyright: © Copyright 1994 American Mathematical Society