Approximate and pseudo-amenability of various classes of Banach algebras

Choi, Yemon and Ghahramani, Fereidoun and Zhang, Yong (2009) Approximate and pseudo-amenability of various classes of Banach algebras. Journal of Functional Analysis, 256 (10). pp. 3158-3191. ISSN 0022-1236

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We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R.J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtained of ℓ1-semigroup algebras which are approximately amenable but not amenable; using these, we show that bounded approximate contractibility need not imply sequential approximate amenability. Results are also given for Segal algebras on locally compact groups, and algebras of p-pseudo-functions on discrete groups.

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Journal Article
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Journal of Functional Analysis
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24 Jan 2014 05:52
Last Modified:
20 Sep 2023 00:35