The amenability constant of the Fourier algebra

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 $\sup \{°(\pi ):\pi \in \hat{G}\}$ and that it is equal to one if and only if $G$ is abelian.

LaTeX2e; 11 pages; some more minor revisions

References in corpus (1)

• Amenability and weak amenability of the Fourier algebra