Metric geometry in homogeneous spaces of the unitary group of a \(C^*\)-algebra. II: Geodesics joining fixed endpoints

DOI10.1007/s00020-003-1305-1zbMath1096.53044OpenAlexW2097122136MaRDI QIDQ814371

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

Publication date: 7 February 2006

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-003-1305-1

zbMATH Keywords

Hopf-Rinow theorem unitary group von Neumann algebras strong operator topology minimal curves uniparametric group curves

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Group structures and generalizations on infinite-dimensional manifolds (58B25) Groups and semigroups of linear operators, their generalizations and applications (47D99) Linear operators in (C^*)- or von Neumann algebras (47C15)

Related Items (9)

Leibniz seminorms and best approximation from \(C^*\)-subalgebras ⋮ Metrics in the sphere of a \(C^*\)-module ⋮ Hopf–Rinow theorem in Grassmann manifolds of C*-algebras ⋮ Projections with fixed difference: a Hopf-Rinow theorem ⋮ Metric geometry of infinite-dimensional Lie groups and their homogeneous spaces ⋮ Minimal curves in \(\mathcal{U}(n)\) and \(\mathcal{G}l(n)^+\) with respect to the spectral and the trace norms ⋮ Geodesic neighborhoods in unitary orbits of self-adjoint operators of \(\mathcal{K}+\mathbb{C}\) ⋮ GEOMETRY OF UNITARIES IN A FINITE ALGEBRA: VARIATION FORMULAS AND CONVEXITY ⋮ Metric geodesics of isometries in a Hilbert space and the extension problem

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