Weak amenability of Fourier algebras on compact groups

Abstract

We give for a compact group G, a full characterisation of when its Fourier algebra A(G) is weakly amenable: when the connected component of the identity G_e is abelian. This condition is also equivalent to the hyper-Tauberian property for A(G), and to having the anti-diagonal D^v={(s,s^{-1}):s is in G} being a set of spectral synthesis for A(GXG). We show the relationship between amenability and weak amenability of A(G), and (operator) amenability and (operator) weak amenability of A_D(G), an algebra defined by the authors in arXiv:0705.4277. We close by extending our results to some classes of non-compact, locally compact groups, including small invariant neighbourhood groups and maximally weakly almost periodic groups.

14 pages

References in corpus (2)

• Convolutions on compact groups and Fourier algebras of coset spaces
• Amenability properties of the centres of group algebras

Cited by in corpus (1)

• Smooth and weak synthesis of the anti-diagonal in Fourier algebras of Lie groups