COHOMOLOGICAL STABILIZATION OF MAXIMAL IDEAL SPACES IN BANACH-ALGEBRAS

[摘要] We prove that for a complex commutative Banach algebra A with finite dimensional character space X, the Bass stable rank condition sr A less-than-or-equal-to n is equivalent to a certain stabilization property for Cech 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 greater-than-or-equal-to 2n + 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. (C) 1994 Academic Press, Inc.

[发布日期] 1994-11-15