Mathematics – Functional Analysis
Scientific paper
2009-06-12
Q. J. Math. (Oxford) 62 (2011), no. 1, 39--58
Mathematics
Functional Analysis
22 pages. v2: minor corrections, updated references. To appear in Q. J. Math. (Oxford)
Scientific paper
10.1093/qmath/hap034
Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for \emph{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 \emph{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.
Choi Yemon
Ghahramani Fereidoun
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