Cohomological stabilization of maximal ideal spaces in Banach algebras
type: Item
instance of: scholarly article
title: Cohomological stabilization of maximal ideal spaces in Banach algebras
zbMATH Open document ID: 0817.46050
author: Daniel Suárez
published in: Journal of Algebra
publication date: 1994-12-14T00:00:00Z
review text: The author proves that for a complex commutative Banach algebra \(A\) with finite dimensional character space \(X\), the Bass stable rank condition \(\text{sr } A\leq n\) 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 \(k\geq 2n+1\). Using this result and Michael's continuous selection theory he improves previous estimations for \(\text{sr } {\mathcal C} (Y,A)\), where \({\mathcal C} (Y,A)\) denotes the algebra of continuous functions from a finite dimensional compact space \(Y\) into \(A\).
Mathematics Subject Classification ID: 46J20
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 46J05
Mathematics Subject Classification ID: 46H05
zbMATH DE Number: 703026
zbMATH Keywords: commutative Banach algebra with finite dimensional character space
zbMATH Keywords: Bass stable rank condition
zbMATH Keywords: stabilization property for Čech cohomology sequences
zbMATH Keywords: Michael's continuous selection theory
MaRDI profile type: Publication
full work available at URL: jabr.1994.1333
OpenAlex ID: W1978147058
DOI: 10.1006/JABR.1994.1333
description: scientific article; zbMATH DE number 703026