The amenability constant of the Fourier algebra

Volker Runde

The amenability constant of the Fourier algebra

Functional Analysis 2007-05-23 v3

Authors: Volker Runde

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

Keywords

locally compact group Fourier algebra amenability constant dual object unitary representations abelian group

Cite

@article{arxiv.math/0409454,
  title  = {The amenability constant of the Fourier algebra},
  author = {Volker Runde},
  journal= {arXiv preprint arXiv:math/0409454},
  year   = {2007}
}

Comments

LaTeX2e; 11 pages; some more minor revisions

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