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arXiv · 1904.03252

(Non-)amenability of the Fourier algebra in the cb-multiplier norm

Volker Runde
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Abstract

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{M_cb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that, if $A_{M_cb}(G)$ is amenable, then $a(G_d)$, the almost periodic compactification of the discretization of $G$, has an abelian subgroup of finite index. As a consequence, $A_{M_cb}(G)$ cannot be amenable if $G$ contains a copy of $\free_2$, the free group in two generators, as a closed subgroup.

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Volker Runde. 2019-04-05. (Non-)amenability of the Fourier algebra in the cb-multiplier norm. https://arxiv.org/abs/1904.03252

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