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Resolution of the cohomology comparison problem for amenable Banach algebras. (English) Zbl 0765.46028
Let \(M\) be a Banach bimodule over a complex Banach algebra \(A\). From the early days of the Banach algebra cohomology up to this day, virtually nothing has been known about the comparison map for the higher cohomology groups. The purpose of this paper is to resolve this question for arbitrary amenable Banach algebras. The following result is given in this paper: If \(\text{card }A=\aleph_ n\) then, for every Banach bimodule \(M\) and any \(q\geq n+3\), the comparison map \(i^ q: {\mathcal H}^ q(A,M)\to H^ q(A,M)\) is zero.

MSC:
46H05 General theory of topological algebras
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
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