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Uniformly Continuous Functionals andM-Weakly Amenable Groups

Published online by Cambridge University Press:  20 November 2018

Brian Forrest
Affiliation:
Department of Pure Mathematics, University of Waterloo, WaterlooON N2L 3G1, e-mail: [email protected]
Tianxuan Miao
Affiliation:
Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON P7B 5E1, e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2013

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