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Uniformly Continuous Functionals andM-Weakly Amenable Groups

Published online by Cambridge University Press:  20 November 2018

Brian Forrest  and
Tianxuan Miao
Brian Forrest
Affiliation:
Department of Pure Mathematics, University of Waterloo, WaterlooON N2L 3G1, e-mail: beforres@math.ualberta.ca
Tianxuan Miao
Affiliation:
Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON P7B 5E1, e-mail: tmiao@lakeheadu.ca
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Abstract

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Let $G$ be a locally compact group. Let ${{A}_{M}}\left( G \right)\,\left( {{A}_{0}}\left( G \right) \right)$ denote the closure of $A\left( G \right)$, the Fourier algebra of $G$ in the space of bounded (completely bounded) multipliers of $A\left( G \right)$. We call a locally compact group $\text{M}$-weakly amenable if ${{A}_{M}}\left( G \right) $ has a bounded approximate identity. We will show that when $G$ is $\text{M}$-weakly amenable, the algebras ${{A}_{M}}\left( G \right) $ and ${{A}_{0}}\left( G \right)$ have properties that are characteristic of the Fourier algebra of an amenable group. Along the way we show that the sets of topologically invariant means associated with these algebras have the same cardinality as those of the Fourier algebra.

Keywords

43A0743A2246J1047L25Fourier algebramultipliersweakly amenableuniformly continuous functionals
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 5 , 01 October 2013 , pp. 1005 - 1019
Copyright
Copyright © Canadian Mathematical Society 2013

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