Approximate and pseudo-amenability of various classes of Banach algebras

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dc.creatorChoi, Y.
dc.creatorGhahramani, F.
dc.creatorZhang, Y.
dc.date2008-01-22
dc.date2009-02-14
dc.date.accessioned2026-07-07T12:56:12Z
dc.date.available2026-07-07T12:56:12Z
dc.descriptionWe continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity. Among our other results, it is shown that the Fourier algebra of the free group on two generators is not approximately amenable. Further examples are obtained of ${\ell}^1$-semigroup algebras which are approximately amenable but not amenable; using these, we show that bounded approximate amenability need not imply sequential approximate amenability. Results are also given for Segal subalgebras of $L^1(G)$, where $G$ is a locally compact group, and the algebras $PF_p(Γ)$ of $p$-pseudofunctions on a discrete group $Γ$ (of which the reduced $C^*$-algebra is a special case).
dc.description35 pages, revision of Jan '08 preprint. Abstract and MSC added; bibliograpy updated; slight tweaks to Section 4; and correction of a few typos. The final version is to appear in J. Funct. Anal
dc.identifierhttps://arxiv.org/abs/0801.3415
dc.identifierhttp://arxiv.org/abs/0801.3415
dc.identifierJ. Funct. Anal. 256 (2009), no. 10, 3158--3191
dc.identifierdoi:10.1016/j.jfa.2009.02.012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224505
dc.subjectFunctional Analysis
dc.titleApproximate and pseudo-amenability of various classes of Banach algebras
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