Orbits of positive operators from a differentiable viewpoint
type: Item
instance of: scholarly article
title: Orbits of positive operators from a differentiable viewpoint
zbMATH Open document ID: 1070.46038
author: Demetrio Stojanoff
author: Gustavo Corach
author: A. Maestripieri
published in: Positivity
publication date: 2004-08-06T00:00:00Z
review text: Let \(\mathcal A\) be a unital \(C^*\)-algebra represented on a Hilbert space \(\mathcal H\), \(G\) be the group of invertible elements of \(\mathcal A\), and \({\mathcal A}^+_{cr}\) the subset of \({\mathcal A}^+\) of positive operators with closed range. In the present paper, the authors study the geometric structure of the orbits \({\mathfrak A}_a=\{gag^*\mid g\in G\}\) corresponding to elements of \({\mathcal A}^+_{cr}\). The authors provide the orbit \({\mathfrak A}_a\) with a structure of a differentiable homogeneous space such that each component belonging to \({\mathfrak A}_a\) remains a submanifold. The case \({\mathfrak A}=L(H)\), the algebra of all bounded linear operators on \(\mathcal H\), is studied in detail in order to show that some changes have to be made in the topology of \({\mathfrak A}_a\) to obtain a structure of that type.
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 2081975
zbMATH Keywords: closed range positive operators
zbMATH Keywords: differential geometry
zbMATH Keywords: Thompson components
reviewed by: Messoud Efendiev
Wikidata QID: Q88554117
MaRDI profile type: Publication
full work available at URL: b:post.0000023202.40428.a8
OpenAlex ID: W2003267352
DOI: 10.1023/B:POST.0000023202.40428.A8
description: scientific article; zbMATH DE number 2081975