Differential geometry of spaces of relatively regular operators
type: Item
instance of: scholarly article
title: Differential geometry of spaces of relatively regular operators
zbMATH Open document ID: 0726.46028
DOI: 10.1007/BF01198917
published in: Integral Equations and Operator Theory
publication date: 1990-01-01T00:00:00Z
review text: Let A be a Banach algebra with group of units G and with the set of idempotents Q. The authors study the topological and geometric properties of the space \(S=\{(a,b)\in A\times A:\) \(ar=a\), \(rb=b\), \(ba=r\}\), where r is a fixed element in Q. In particular they study principal fiber bundles \(\tau: G\to S\), where \(\tau (g)=(ga_ 0,b_ 0g^{-1}),\) \((a_ 0,b_ 0)\in S\), and \(\theta: S\to Q,\) where \(\theta ((a,b))=ab.\) When A is a \(C^*\)-algebra and \(r=r^*\), they study also a real analytic retraction of S onto \(\{\) (a,b)\(\in S:\) \(b=a^*\}\). The authors announce further papers on similar topics.
Mathematics Subject Classification ID: 46H05
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 53C99
zbMATH DE Number: 4198818
zbMATH Keywords: principal fiber bundles
zbMATH Keywords: real analytic retraction
Wikidata QID: Q115393918
author: Gustavo Corach
author: Horacio Porta
author: Lázaro Recht
reviewed by: Wiesław Tadeusz Żelazko
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01198917
OpenAlex ID: W2010324047
description: scientific article; zbMATH DE number 4198818