Natural variational problems in the Grassmann manifold of a \(C^*\)-algebra with trace

DOI10.1006/aima.2000.1924zbMath0977.58014OpenAlexW2068257176MaRDI QIDQ1584530

Lázaro Recht, Luis E. Mata-Lorenzo, Carlos Eduardo Durán

Publication date: 11 March 2001

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aima.2000.1924

zbMATH Keywords

geodesicsGrassmann manifoldFinsler metrics

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) General theory of (C^*)-algebras (46L05) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (7)

Weakly invariant norms: geometry of spheres in the space of skew-Hermitian matrices ⋮ Moving planes, Jacobi curves and the dynamical approach to Finsler geometry ⋮ Metric geometry of partial isometries in a finite von Neumann algebra ⋮ Homogeneous manifolds from noncommutative measure spaces ⋮ Metric geometry of infinite-dimensional Lie groups and their homogeneous spaces ⋮ Finsler geometry and actions of the $p$-Schatten unitary groups ⋮ GEOMETRY OF UNITARIES IN A FINITE ALGEBRA: VARIATION FORMULAS AND CONVEXITY

Cites Work

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• Notes on non-commutative integration
• The geometry of spaces of projections in \(C^*\)-algebras
• Convexity properties of \(tr[(a^*a)^n\)]
• Isometric submersions of Finsler manifolds
• Minimality of Geodesics in Grassmann Manifolds
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen

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