Amenability and derivations of the Fourier algebra

Author:

Forrest Brian

Abstract

It is shown that a locally compact group G G is amenable if and only if every derivation of the Fourier algebra A ( G ) A(G) into a Banach A ( G ) A(G) -bimodule is continuous. Also given are necessary and sufficient conditions for A ( G ) A(G) to be weakly amenable.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference8 articles.

1. W. G. Bade, P. C. Curtis and H. Dales, Amenability and weak amenability for Beurling and Lipschitz algebras (preprint).

2. Cofinite ideals in Banach algebras, and finite-dimensional representations of group algebras;Dales, H. G.,1983

3. L’algèbre de Fourier d’un groupe localement compact;Eymard, Pierre;Bull. Soc. Math. France,1964

4. B. Forrest, Amenability and bounded approximate identities in ideals of 𝐴(𝐺) (preprint).

5. Weakly almost periodic and uniformly continuous functionals on the Fourier algebra of any locally compact group;Granirer, Edmond E.;Trans. Amer. Math. Soc.,1974

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