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

作者：Lee Hun Hee^*; Ludwig Jean; Samei Ebrahim; Spronk Nico

来源：Advances in Mathematics, 2016, 292: 11-41.

DOI：10.1016/j.aim.2016.01.005

• Fourier algebra
• Weak amenability
• Local synthesis

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, Delta G = {(g, g(-1)) : g is an element of G} is a set of local synthesis for A(G x 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.

• 出版日期2016-4-9
• 单位Saskatoon; Saskatchewan