Natural variational problems in the Grassmann manifold of a \(C^*\)-algebra with trace
type: Item
instance of: scholarly article
title: Natural variational problems in the Grassmann manifold of a \(C^*\)-algebra with trace
zbMATH Open document ID: 0977.58014
author: Luis E. Mata-Lorenzo
author: Lázaro Recht
author: Carlos E. Durán
published in: Advances in Mathematics
publication date: 2001-03-11T00:00:00Z
review text: The authors introduce a new Finsler structure of the Grassmann manifold of a \(C^*\)-algebra with trace and they study its convex properties. The main results of the paper describe the geodesic structure of this manifold. Among other things the authors prove that the extremals are the usual geodesics. A minimality theorem for some geodesics is also established. In an appendix, an interesting discussion concerning the equivalence of two approaches for the definition of length of an arc is provided.
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 1525154
zbMATH Keywords: Finsler metrics
zbMATH Keywords: Grassmann manifold
zbMATH Keywords: geodesics
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
full work available at URL: aima.2000.1924
OpenAlex ID: W2068257176
cites work: Q3263053
cites work: Q5735422
cites work: Q5538494
cites work: Interpolation zwischen den Klassen 𝔖p von Operatoren in Hilberträumen
cites work: Notes on non-commutative integration
cites work: Q3667432
cites work: Minimality of Geodesics in Grassmann Manifolds
cites work: Q3797713
cites work: Q3985446
cites work: Q4014029
cites work: The geometry of spaces of projections in \(C^*\)-algebras
cites work: Q4893267
cites work: Isometric submersions of Finsler manifolds
cites work: Convexity properties of \(tr[(a^*a)^n]\)
DOI: 10.1006/AIMA.2000.1924
description: scientific article; zbMATH DE number 1525154