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Uniformly Continuous Functionals and M-Weakly Amenable Groups
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- Journal:
- Canadian Journal of Mathematics / Volume 65 / Issue 5 / 01 October 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1005-1019
- Print publication:
- 01 October 2013
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- Article
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- You have access
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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.
