Geometric representation theory for unitary groups of operator algebras

DOI10.1016/j.aim.2006.02.009zbMath1108.22008arXivmath/0501057OpenAlexW2085279325MaRDI QIDQ854104

Daniel Beltiţă, Tudor S. Ratiu

Publication date: 7 December 2006

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

Full work available at URL: https://arxiv.org/abs/math/0501057

zbMATH Keywords

Banach algebravon Neumann algebraunitary representationreproducing kerneloperator algebrahomogeneous vector bundleGNS constructiongeometric realizationspace of sectionsUnitary group

Mathematics Subject Classification ID

Representations of topological algebras with involution (46K10) Harmonic analysis on homogeneous spaces (43A85) General theory of von Neumann algebras (46L10) Semisimple Lie groups and their representations (22E46) General theory of (C^*)-algebras (46L05) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) States of selfadjoint operator algebras (46L30) Questions of holomorphy and infinite-dimensional manifolds (58B12)

Related Items (11)

Geometric Perspectives on Reproducing Kernels ⋮ Coadjoint Orbits and the Beginnings of a Geometric Representation Theory ⋮ Lie theoretic significance of the measure topologies associated with a finite trace ⋮ Linear connections for reproducing kernels on vector bundles ⋮ Holomorphic geometric models for representations of \(C^*\)-algebras ⋮ Universal objects in categories of reproducing kernels ⋮ GEOMETRIC CHARACTERIZATION OF HERMITIAN ALGEBRAS WITH CONTINUOUS INVERSION ⋮ Manifolds of classical probability distributions and quantum density operators in infinite dimensions ⋮ Iwasawa decompositions of some infinite-dimensional Lie groups ⋮ Coherent state map quantization in a Hermitian-like setting ⋮ Holomorphic Realization of Unitary Representations of Banach–Lie Groups

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