Cohomological Stabilization of Maximal Ideal Spaces in Banach Algebras Original Research Article

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 imageech 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 ≥ 2n + 1. Using this result and Michael′s continuous selection theory we improve previous estimations for sr image(Y, A), where image(Y, A) denotes the algebra of continuous functions from a finite dimensional compact space Y into A.