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

Volker Runde

Published 2019-04-05Version 1

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 $A_{Mcb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that $A_{Mcb}(G)$ is not amenable if $G$ contains a copy of the free group in two generators as a closed subgroup.