Article Dans Une Revue Advances in Mathematics Année : 2016

Weak amenability of Fourier algebras and local synthesis of the anti-diagonal

Résumé

We show that for a connected Lie group G, its Fourier algebra is weakly amenable only if G is abelian. Our main new idea is to show that weak amenability of implies that the anti-diagonal, , is a set of local synthesis for . We then show that this cannot happen if G is non-abelian. We conclude for a locally compact group G, that can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group G, is weakly amenable if and only if its connected component of the identity is abelian.

Dates et versions

hal-03313480 , version 1 (04-08-2021)

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Hun Hee Lee, Jean Ludwig, Ebrahim Samei, Nico Spronk. Weak amenability of Fourier algebras and local synthesis of the anti-diagonal. Advances in Mathematics, 2016, 292, pp.11-41. ⟨10.1016/j.aim.2016.01.005⟩. ⟨hal-03313480⟩
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