2003/11/28 by Niels Grønbæk, Grønbæk, Niels
Mathematics · #16E40 (Secondary) #46M20 (Primary) 47B09 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:16E40 #msc:46M20 #msc:47B09
paper · pdf · doi:10.48550/arxiv.math/0311529
12 pages, submitted to journal
arxiv created 2003/11/28 · openalex publication_date 2003/11/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Hn(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, L1(μ,Ω) is an infinite dimensional L1-space, and A is the Banach algebra of approximable operators on Lp(X,μ,Ω), (1==0.