Extension problems and stable rank in commutative Banach algebras
type: Item
instance of: scholarly article
title: Extension problems and stable rank in commutative Banach algebras
zbMATH Open document ID: 0606.46033
DOI: 10.1016/0166-8641(85)90052-5
author: Gustavo Corach
author: Daniel Suárez
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: The concept of stable rank was introduced by H. Bass. In recent papers of G. Corach (with the collaboration of F. D. Suarez and A. R. Larotonda) stable rank conditions on a Banach algebra are related to the topology of its spectrum. In these two papers the authors applied previous results and algebraic- topological properties to estimate the stable rank of commutative Banach algebras; in particular, holomorphic function algebras. For example, in the first paper they show that the topological stable rank of \(A(\Delta^ n)\) is \(n+1\) while in the second they show that the (Bass) stable rank of this algebra lies between \([n/2]+1\) and n. Several open problems are stated, in particular, to calculate the exact value of the topological stable rank of \(A(\Delta^ n)\) for \(n\geq 3\).
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 46J05
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 3979783
zbMATH Keywords: unimodular
zbMATH Keywords: polydisc
zbMATH Keywords: stable rank
zbMATH Keywords: holomorphic function algebras
zbMATH Keywords: calculate the exact value of the topological stable rank
reviewed by: Guillermo López Lagomasino
MaRDI profile type: Publication
full work available at URL: 0166-8641(85)90052-5
OpenAlex ID: W2052755482
cites work: Q5182686
cites work: \(K\)-theory and stable algebra
cites work: Interpolations by bounded analytic functions and the corona problem
cites work: Stable range in Banach algebras
cites work: A stabilization theorem for Banach algebras
cites work: Lower bounds on the stable range of polynomial rings
cites work: The stable range of \(C^*\)-algebras
cites work: Q5802788
cites work: Stable Rank of the Disc Algebra
cites work: Convex Structures and Continuous Selections
cites work: Q3667577
cites work: Q5575015
cites work: Homotopy theory of infinite dimensional manifolds
cites work: Dimension and Stable Rank in the K -Theory of C* -Algebras
cites work: Q5667036
cites work: Topological Examples of Projective Modules
cites work: Topological invariants of the maximal ideal space of a Banach algebra
cites work: Stable rank of rings and dimensionality of topological spaces
cites work: SERRE'S PROBLEM ON PROJECTIVE MODULES OVER POLYNOMIAL RINGS, AND ALGEBRAIC $ K$-THEORY
Wikidata QID: Q127628852
description: scientific article; zbMATH DE number 3979783