Differential geometry of partial isometries and partial unitaries
type: Item
instance of: scholarly article
title: Differential geometry of partial isometries and partial unitaries
zbMATH Open document ID: 1044.46044
author: Esteban Andruchow
author: Gustavo Corach
published in: Illinois Journal of Mathematics
publication date: 2004-03-17T00:00:00Z
review text: For a \(C^*\)-algebra \(A\), the sets \(I\) of partial isometries and \(I_\Delta\subset I\) of partial unitaries (i.e., partial isometries that commute with their adjoints) are submanifolds of \(A\). The space \(I\) is a homogeneous reductive space of the group \(U_A\times U_A\), where \(U_A\) is the unitary group of \(A\), and geodesics are computed in a standard fashion. A condition is given for existence of geodesics joining two endpoints. A principal bundle with base \(I_\Delta\) is introduced and a natural connection is defined. Additional data enable the authors to construct a linear connection on \(I_\Delta\) and to characterize its geodesics.
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 53B99
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 2060303
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: partial isometry
zbMATH Keywords: linear connection
zbMATH Keywords: geodesics
reviewed by: Vladimir M. Manuilov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2060303