Translation invariant functionals on Lp (G) when G is not amenable-Reference-Cited by-同舟云学术

Translation invariant functionals on Lp (G) when G is not amenable

Published:1986-10 Issue:2 Volume:41 Page:237-250
ISSN:0263-6115
Container-title:Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
language:en
Short-container-title:J Aust Math Soc A

Author:

Willis G. A.

Abstract

AbstractIt is shown that if G is a non-amenable group, then there are no non-zero translation invariant functionals on Lp(G) for 1 < p < ∞. Furthermore, if G contains a closed, non-abelian free subgroup, then there are no non-zero translation invariant functionals on C0(G). The latter is proved by showing that a certain non-invertible convolution operator on C0(G) is surjective.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics,Statistics and Probability

Reference12 articles.

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4. L1-Algebras and Segal Algebras

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