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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Amenability and the structure of the algebras $ A\sb p(G)$


Author: Brian Forrest
Journal: Trans. Amer. Math. Soc. 343 (1994), 233-243
MSC: Primary 43A07; Secondary 43A15, 46J99
MathSciNet review: 1181182
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Abstract: A number of characterizations are given of the class of amenable locally compact groups in terms of the ideal structure of the algebras $ {A_p}(G)$. An almost connected group is amenable if and only if for some $ 1 < p < \infty $ and some closed ideal I of $ {A_p}(G)$, I has a bounded approximate identity. Furthermore, G is amenable if and only if every derivation of $ {A_p}(G)$ into a Banach $ {A_p}(G)$-bimodule is continuous.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1181182-5
PII: S 0002-9947(1994)1181182-5
Keywords: Amenable groups, Herz algebra, bounded approximate identities, ideal, automatic continuity, derivations
Article copyright: © Copyright 1994 American Mathematical Society