The geometry of spaces of projections in \(C^*\)-algebras
type: Item
instance of: scholarly article
title: The geometry of spaces of projections in \(C^*\)-algebras
zbMATH Open document ID: 0799.46067
published in: Advances in Mathematics
publication date: 1994-11-17T00:00:00Z
review text: Let \(A\) be a \(C^*\)-algebra with identity represented as an algebra of operators in a Hilbert space \(E\). The authors give the geometric structure of the space \(\mathbb{Q}\) of idempotent elements of \(A\). Particular attention is devoted to the way \(Q\) is fibred over the space \(P\) of all selfadjoint elements of \(Q\). The set \(Q\) inherits from \(A\) a differentiable structure with a natural connection. The resulting retraction \(\pi : Q \to P\) is given by the polar decomposition of the associated symmetries, and alternative characterization of the fibres \(\mathbb{Q}_ p = \pi^{-1} (p)\) are presented. The authors also considered metric properties. A Finsler structure naturally related to \(Q@> \pi>> P\) is introduced in \(Q\) and the final part is devoted to the study of geodesics in \(Q\).
reviewed by: Bolis Basit
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 495496
zbMATH Keywords: \(C^*\)-algebra with identity
zbMATH Keywords: geometric structure of the space of idempotent elements
zbMATH Keywords: differentiable structure
zbMATH Keywords: connection
zbMATH Keywords: polar decomposition
author: Gustavo Corach
author: Horacio Porta
author: Lázaro Recht
MaRDI profile type: Publication
full work available at URL: aima.1993.1041
OpenAlex ID: W2052950215
DOI: 10.1006/AIMA.1993.1041
description: scientific article; zbMATH DE number 495496