GEOMETRY OF UNITARIES IN A FINITE ALGEBRA: VARIATION FORMULAS AND CONVEXITY

DOI10.1142/S0129167X08005102zbMath1169.46029MaRDI QIDQ5506285

Esteban Andruchow, Lázaro Recht

Publication date: 28 January 2009

Published in: International Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

\(C^*\)-algebratraceunitary groupFinsler metricgeodesic distancevariation formulas\(p\)-energy functional

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Noncommutative measure and integration (46L51) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Group structures and generalizations on infinite-dimensional manifolds (58B25)

Related Items (7)

Finsler geometries on strictly accretive matrices ⋮ Geometry of infinite dimensional unitary groups: convexity and fixed points ⋮ Metric geometry of partial isometries in a finite von Neumann algebra ⋮ Homogeneous manifolds from noncommutative measure spaces ⋮ Minimal curves in \(\mathcal{U}(n)\) and \(\mathcal{G}l(n)^+\) with respect to the spectral and the trace norms ⋮ Weak Riemannian manifolds from finite index subfactors ⋮ Finsler geometry and actions of the $p$-Schatten unitary groups

Cites Work

• Unnamed Item
• Metric geometry in homogeneous spaces of the unitary group of a \(C^*\)-algebra. II: Geodesics joining fixed endpoints
• Convexity properties of \(tr[(a^*a)^n\)]
• Natural variational problems in the Grassmann manifold of a \(C^*\)-algebra with trace
• Metric geometry in homogeneous spaces of the unitary group of a \(C^*\)-algebra. I: Minimal curves
• Short Geodesics of Unitaries in the L² Metric
• GRASSMANNIANS OF A FINITE ALGEBRA IN THE STRONG OPERATOR TOPOLOGY

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