Hopf–Rinow theorem in Grassmann manifolds of C*-algebras

DOI10.1007/978-3-030-34072-8_15zbMath1443.53001OpenAlexW2989890738MaRDI QIDQ3294714

Eduardo Chiumiento

Publication date: 29 June 2020

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

Full work available at URL: https://doi.org/10.1007/978-3-030-34072-8_15

zbMATH Keywords

compact operatorGrassmann manifoldrestricted Grassmannianminimal geodesic\(C^\ast \)-algebra

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Topological (rings and) algebras with an involution (46K99)

Cites Work

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• Essentially commuting projections
• Pairs of projections: geodesics, Fredholm and compact pairs
• Metric geometry in homogeneous spaces of the unitary group of a \(C^*\)-algebra. II: Geodesics joining fixed endpoints
• Hopf-Rinow theorem in the Sato Grassmannian
• Geometric significance of Toeplitz kernels
• Metric geometry in homogeneous spaces of the unitary group of a \(C^*\)-algebra. I: Minimal curves
• Optimal paths for symmetric actions in the unitary group
• Metric geometry of infinite-dimensional Lie groups and their homogeneous spaces
• Minimality of Geodesics in Grassmann Manifolds
• The Hopf-Rinow Theorem is false in infinite Dimensions
• Hilbert Manifolds Without Epiconjugate Points
• Two Subspaces

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