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- W1720803042 abstract "We show that for a connected Lie group $G$, its Fourier algebra $A(G)$ is weakly amenable only if $G$ is abelian. Our main new idea is to show that weak amenability of $A(G)$ implies that the anti-diagonal, $check{Delta}_G={(g,g^{-1}):gin G}$, is a set of local synthesis for $A(Gtimes G)$. We then show that this cannot happen if $G$ is non-abelian. We conclude for a locally compact group $G$, that $A(G)$ can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group $G$, $A(G)$ is weakly amenable if and only if its connected component of the identity $G_e$ is abelian." @default.
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- W1720803042 date "2015-02-18" @default.
- W1720803042 modified "2023-10-07" @default.
- W1720803042 title "Weak amenability of Fourier algebras and local synthesis of the anti-diagonal" @default.
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