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

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

G. A. Willis
G. A. Willis
Affiliation:
Department of Pure Mathematics, The University of Adelaide, Box 498 G.P.O., Adelaide S.A. 5001, Australia
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Abstract

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It 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.

MSC classification

Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 2 , October 1986 , pp. 237 - 250
Copyright
Copyright © Australian Mathematical Society 1986

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