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Computing and estimating the global dimension in certain classes of Banach algebras. (English) Zbl 0830.46066
Let \(A\) be a (nonzero) Banach algebra. The author studies the homological dimension of the Banach \(A\)-module \(M_+ (A)\) of right multipliers on \(A\). In the case, when \(dh_A (A)= n<+ \infty\), it is shown that \(dh_A M_+ (A)\leq n+2\). It turns out that under some natural conditions this inequality becomes equality. Besides of these specific results the paper contains some other results on homological dimension.

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