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

2006
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Transactions of the American Mathematical Society
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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 cohomology H n (A, A * ) vanishes for all n ≥ 1. The hypotheses of this theorem involve (i) strong H-unitality of A, (ii) a growth condition on diagonal matrices in A, and (iii) an extension of A in B by an amenable Banach algebra. As a corollary we show that if X is an

doi:10.1090/s0002-9947-06-03913-4
fatcat:3urzad6izjhntpix5kngbg3ohq