Bounded Hochschild cohomology of Banach algebras with a matrix-like structure

dc.creatorGrønbæk, Niels
dc.date2003-11-28
dc.date.accessioned2026-07-07T05:03:23Z
dc.date.available2026-07-07T05:03:23Z
dc.descriptionLet B be a unital Banach algebra. A projection in B which is equivalent to the identitity may give rise to a matrix-like structure on any two-sided ideal A in B. In this set-up we prove a theorem to the effect that the bounded Hochschild cohomology H^n(A,A^*) vanishes for all n>=1. The hypothesis of this theorem involve (i) strong H-unitality of A, (ii) a growth condition on diagonal matrices in A, (iii) an extension of A in B with trivial bounded simplicial homology. As a corollary we show that if X is an infinite dimensional Banach space with the bounded approximation property, L_1(μ,Ω) is an infinite dimensional L_1-space, and A is the Banach algebra of approximable operators on L_p(X,μ,Ω), (1=<p<\infty), then H^n(A,A^*)=(0) for all n>=0.
dc.description12 pages, submitted to journal
dc.identifierhttps://arxiv.org/abs/math/0311529
dc.identifierhttp://arxiv.org/abs/math/0311529
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69394
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subject46M20 (Primary) 47B09, 16E40 (Secondary)
dc.titleBounded Hochschild cohomology of Banach algebras with a matrix-like structure
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