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The amenability constant of the Fourier algebra

Volker Runde
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Abstract

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra and $\hat{G}$ its dual object, i.e. the collection of equivalence classes of unitary represenations of $G$. We show that the amenability constant of $A(G)$ is less than or equal to $\sup \{°(π) : π\in \hat{G} \}$ and that it is equal to one if and only if $G$ is abelian.

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Volker Runde. 2005-01-06. The amenability constant of the Fourier algebra. https://arxiv.org/abs/math/0409454

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