Choi, Yemon and Ghahramani, Fereidoun (2011) Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras. The Quarterly Journal of Mathematics, 62 (1). pp. 39-58. ISSN 0033-5606
Full text not available from this repository.Abstract
Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for approximate amenability have been open for some years now. In this article we give a complete solution for the first two classes, using a new criterion for showing that certain Banach algebras without bounded approximate identities cannot be approximately amenable. The method also provides a unified approach to existing non-approximate amenability results, and is applied to the study of certain commutative Segal algebras. Using different techniques, we prove that bounded approximate amenability of the second dual of a Fourier algebra implies that it is finite-dimensional. Some other results for related algebras are obtained.