Unitary invariants for Hilbert modules of finite rank

DOI10.1515/CRELLE.2011.091zbMath1243.46063arXiv0909.1902MaRDI QIDQ3117036

Gadadhar Misra, Mihai Putinar, Shibananda Biswas

Publication date: 16 February 2012

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.1902

zbMATH Keywords

linear spaceresolutionHilbert modulecoherent sheafsubmodulereproducing kernel functionGleason problemholomorphic Hermitian vector bundleanalytic Hilbert moduleprivilege

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Bergman spaces of functions in several complex variables (32A36) Holomorphic functions of several complex variables (32A10) Algebras of holomorphic functions of several complex variables (32A38) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (7)

The eigensheaf of an operator ⋮ Geometric invariants for a class of submodules of analytic Hilbert modules via the sheaf model ⋮ \(K\)-invariant Hilbert modules and singular vector bundles on bounded symmetric domains ⋮ Stratified Hilbert modules on bounded symmetric domains ⋮ A local theory for operator tuples in the Cowen-Douglas class ⋮ Survey of last ten years of work done in India in some selected areas of functional analysis and operator theory ⋮ Hilbert modules and complex analytic fibre spaces

Cites Work

• The Fredholm index of a pair of commuting operators. II
• Spectral theory and sheaf theory. II
• Toeplitz operators in several complex variables
• On the index of Toeplitz operators of several complex variables
• Quasi-free resolution of Hilbert modules
• Lineare Faserräume und kohärente Modulgarben über komplexen Räumen
• Fredholm operators associated with strongly pseudoconvex domains in \(C^n\)
• Generalized Bergman Kernels and the Cowen-Douglas Theory
• Sharp Kernels and Canonical Subspaces (Revised)
• On the Rigidity of Bergman Submodules
• Algebraic Reduction and Rigidity for Hilbert Modules
• Complex geometry and operator theory

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