Abstract
We prove that for a complex commutative Banach algebra A with finite dimensional character space X, the Bass stable rank condition sr A ≤ n is equivalent to a certain stabilization property for Čech cohomology sequences of pairs ( X, Z), where Z is the hull of an arbitrary closed ideal. In particular, the k-cohomology groups of X, Z and ( X, Z) vanish when k ≥ 2 n + 1. Using this result and Michael′s continuous selection theory we improve previous estimations for sr C ( Y, A), where C ( Y, A) denotes the algebra of continuous functions from a finite dimensional compact space Y into A.
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