Finsler geometry and actions of the $p$-Schatten unitary groups

DOI10.1090/S0002-9947-09-04877-6zbMath1182.22011arXiv0808.2274MaRDI QIDQ3402202

Esteban Andruchow, Lázaro Recht, Gabriel Larotonda

Publication date: 2 February 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.2274

zbMATH Keywords

homogeneous spaceshort geodesic\(p\)-Schatten classclassical Banach-Lie group

Mathematics Subject Classification ID

Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50)

Related Items (16)

Finsler geometries on strictly accretive matrices ⋮ Weakly invariant norms: geometry of spheres in the space of skew-Hermitian matrices ⋮ Geometry of infinite dimensional unitary groups: convexity and fixed points ⋮ Unitary group orbits versus groupoid orbits of normal operators ⋮ Unitary subgroups and orbits of compact self-adjoint operators ⋮ Homogeneous manifolds from noncommutative measure spaces ⋮ Optimal paths for symmetric actions in the unitary group ⋮ Metric geometry in infinite dimensional Stiefel manifolds ⋮ Best approximation by diagonal operators in Schatten ideals ⋮ 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 ⋮ Lagrangian Grassmannian in infinite dimension ⋮ On restricted diagonalization ⋮ Canonical sphere bundles of the Grassmann manifold ⋮ Geodesics of projections in von Neumann algebras ⋮ Large scale geometry of Banach-Lie groups

Cites Work

• Some considerations on topologies of infinite dimensional unitary coadjoint orbits
• The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits
• Hopf-Rinow theorem in the Sato Grassmannian
• Loop groups and equations of KdV type
• A note on norm ideals and the operator \(X\to AX-XB\)
• The relationship between a commutative Banach algebra and its maximal ideal space
• An estimate for Lipschitz constants of metric projections
• The geometry of spaces of projections in \(C^*\)-algebras
• Convexity properties of \(tr[(a^*a)^n\)]
• Natural variational problems in the Grassmann manifold of a \(C^*\)-algebra with trace
• Unitary orbits in a full matrix algebra
• Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space
• Minimality of Geodesics in Grassmann Manifolds
• GEOMETRY OF UNITARIES IN A FINITE ALGEBRA: VARIATION FORMULAS AND CONVEXITY
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Finsler geometry and actions of the $p$-Schatten unitary groups