Bounded Hochschild cohomology of Banach algebras with a matrix-like structure
| dc.creator | Grønbæk, Niels | |
| dc.date | 2003-11-28 | |
| dc.date.accessioned | 2026-07-07T05:03:23Z | |
| dc.date.available | 2026-07-07T05:03:23Z | |
| dc.description | Let 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.description | 12 pages, submitted to journal | |
| dc.identifier | https://arxiv.org/abs/math/0311529 | |
| dc.identifier | http://arxiv.org/abs/math/0311529 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69394 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46M20 (Primary) 47B09, 16E40 (Secondary) | |
| dc.title | Bounded Hochschild cohomology of Banach algebras with a matrix-like structure | |
| dc.type | text |