A stabilization theorem for Banach algebras
type: Item
instance of: scholarly article
title: A stabilization theorem for Banach algebras
zbMATH Open document ID: 0603.18006
DOI: 10.1016/0021-8693(86)90203-6
author: Gustavo Corach
author: Angel R. Larotonda
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: The paper deals with Bass' stable rank of a (real or complex) Banach algebra. The result mentioned in the title is the following: the sequence \(\{\pi_ i(GL_ m(A))\}_ m\) stabilizes when \(m\geq sr(A)+i+1\) where sr(A) is Bass' stable rank of A. This means that \(K_ i^{top}(A)=\pi_{i-1}(GL_ m(A))\) for those m. The proof is based on a theorem which has some interest in itself: if X is a compact space with topological dimension d and A(X) denotes the Banach algebra of all maps \(X\to A\), then \(sr(A(X))\leq sr(A)+d.\) For related results and methods, see \textit{M. Rieffel} [Proc. Lond. Math. Soc., III. Ser. 46, 301-333 (1983; Zbl 0533.46046)] and \textit{H. Schröder} [Math. Ann. 267, 271-277 (1984; Zbl 0525.46040)].
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 16Exx
Mathematics Subject Classification ID: 46H25
zbMATH DE Number: 3973122
zbMATH Keywords: Bass' stable rank
zbMATH Keywords: Banach algebra
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90203-6
OpenAlex ID: W2039835355
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description: scientific article; zbMATH DE number 3973122