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# Uniformly Continuous Functionals and M-Weakly Amenable Groups

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Published:2013-07-19
Printed: Oct 2013
• Brian Forrest,
Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1
• Tianxuan Miao,
Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON P7B 5E1
 Format: LaTeX MathJax PDF

## Abstract

Let $G$ be a locally compact group. Let $A_{M}(G)$ ($A_{0}(G)$)denote the closure of $A(G)$, the Fourier algebra of $G$ in the space of bounded (completely bounded) multipliers of $A(G)$. We call a locally compact group M-weakly amenable if $A_M(G)$ has a bounded approximate identity. We will show that when $G$ is M-weakly amenable, the algebras $A_{M}(G)$ and $A_{0}(G)$ have properties that are characteristic of the Fourier algebra of an amenable group. Along the way we show that the sets of tolopolically invariant means associated with these algebras have the same cardinality as those of the Fourier algebra.
 Keywords: Fourier algebra, multipliers, weakly amenable, uniformly continuous functionals
 MSC Classifications: 43A07 - Means on groups, semigroups, etc.; amenable groups 43A22 - Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 46J10 - Banach algebras of continuous functions, function algebras [See also 46E25] 47L25 - Operator spaces (= matricially normed spaces) [See also 46L07]

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