The amenability constant of the Fourier algebra

Runde, Volker

doi:10.1090/S0002-9939-05-08164-5

The amenability constant of the Fourier algebra
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by Volker Runde

Proc. Amer. Math. Soc. 134 (2006), 1473-1481

DOI: https://doi.org/10.1090/S0002-9939-05-08164-5

Published electronically: October 18, 2005

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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 representations of $G$. We show that the amenability constant of $A(G)$ is less than or equal to $\sup \{ \deg (\pi ) : \pi \in \hat {G} \}$ and that it is equal to one if and only if $G$ is abelian.

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