Iwasawa decompositions of some infinite-dimensional Lie groups

DOI10.1090/S0002-9947-09-04824-7zbMath1182.22012arXivmath/0701404OpenAlexW2594165529WikidataQ115289046 ScholiaQ115289046MaRDI QIDQ3648210

Daniel Beltiţă

Publication date: 24 November 2009

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

Full work available at URL: https://arxiv.org/abs/math/0701404

zbMATH Keywords

Lie groupIwasawa decompositionoperator idealtriangular integral

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Semisimple Lie groups and their representations (22E46) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Group structures and generalizations on infinite-dimensional manifolds (58B25) Operator ideals (47L20)

Related Items (5)

Covariant representations for possibly singular actions on $C^*$-algebras ⋮ Infinite dimensional symmetric spaces and Lax equations compatible with the infinite Toda chain ⋮ Banach Poisson-Lie groups and Bruhat-Poisson structure of the restricted Grassmannian ⋮ On restricted diagonalization ⋮ On the Iwasawa decomposition of a perplectic matrix

Cites Work

• Geometric representation theory for unitary groups of operator algebras
• Amenability, completely bounded projections, dynamical systems and smooth orbits
• Factorization in analytic operator algebras
• Nest algebras and similarity transformations
• Coordinates for triangular operators algebras
• Method of holomorphic extensions in the theory of unitary representations of infinite-dimensional classical groups
• Factorization problems for nests: Factorization methods and characterizations of the universal factorization property
• Representation theory of the Hilbert-Lie group U(H)//2
• Interpolation problems in nest algebras
• Linear algebraic groups in infinite dimensions
• Some remarks on interpolation theorems and the boundness or the triangular projection in unitary matrix spaces
• Unitary highest weight representations in Hilbert spaces of holomorphic functions on infinite dimensional domains
• An infinite dimensional version of the Schur-Horn convexity theorem
• A Schur-Horn-Kostant convexity theorem for the diffeomorphism group of the annulus
• An infinite dimensional version of the Kostant convexity theorem.
• Birkhoff decompositions and Iwasawa decompositions for loop groups
• Separable representations for automorphism groups of infinite symmetric spaces
• Commutator structure of operator ideals
• A Cartan-Hadamard theorem for Banach-Finsler manifolds
• Simple \(L^*\)-algebras of classical type
• Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space
• Symplectic leaves in real Banach Lie-Poisson spaces
• On some types of topological groups
• The Bott–Borel–Weil Theorem for direct limit groups
• The Structure of a Class of Representations of the Unitary Group on a Hilbert Space
• Principal series representations of direct limit groups
• On the Nonlinear Convexity Theorem of Kostant
• On convexity, the Weyl group and the Iwasawa decomposition
• On Amenability and Geometry of Spaces of Bounded Representations
• Holomorphic highest weight representations of infinite dimensional complex classical groups
• Traces, ideals, and arithmetic means
• A Bott-Borel-Weil theory for direct limits of algebraic groups
• Analyticity in Operator Algebras
• GENERALISING GROUP ALGEBRAS
• Lie groups beyond an introduction
• Lie algebras of bounded operators
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Iwasawa decompositions of some infinite-dimensional Lie groups