Similarity implies homotopy of idempotents in Banach algebras of stable rank one
type: Item
instance of: scholarly article
title: Similarity implies homotopy of idempotents in Banach algebras of stable rank one
zbMATH Open document ID: 1122.19002
author: Julien Giol
published in: Archiv der Mathematik
publication date: 2007-03-20T00:00:00Z
review text: According to \textit{M. A. Rieffel} [``Dimension and stable rank in the \(K\)-theory of \(C^{*}\)-algebras'', Proc. Lond. Math. Soc. (3) 46, 301--333 (1983; Zbl 0533.46046)] a real Banach algebra \(A\) has stable rank one if and only if the set \(A^{-1}\) of invertible elements in \(A\) on dense in \(A\). In this paper the latter property is considered as a definition and the following results is proved: In a real Banach algebra of stable rank one, any two similar idempotents can be connected by a piecewise affine homotopy consisting of at most 3 affine steps.
reviewed by: Liliana Răileanu
Mathematics Subject Classification ID: 19A99
Mathematics Subject Classification ID: 46H20
zbMATH DE Number: 5135802
zbMATH Keywords: Idempotent
zbMATH Keywords: Similarity
zbMATH Keywords: Homotopy
zbMATH Keywords: piecewise affine path
MaRDI profile type: Publication
full work available at URL: s00013-006-1891-7
OpenAlex ID: W2098008177
DOI: 10.1007/S00013-006-1891-7
description: scientific article; zbMATH DE number 5135802