Functional models of \(\Gamma_n\)-contractions and characterization of \(\Gamma_n\)-isometries

DOI10.1016/j.jfa.2014.02.034zbMath1295.32010arXiv1301.2837OpenAlexW57389619MaRDI QIDQ2512376

Shibananda Biswas, Subrata Shyam Roy

Publication date: 7 August 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.2837

zbMATH Keywords

polydiscweighted Bergman spacesymmetrized polydisc

Mathematics Subject Classification ID

Bergman spaces of functions in several complex variables (32A36) Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) (32A37) Canonical models for contractions and nonselfadjoint linear operators (47A45)

Related Items (16)

Characterizations of symmetrized polydisc ⋮ Dilation, functional model and a complete unitary invariant for C.0Γn-contractions ⋮ On reducing submodules of Hilbert modules with \(\mathfrak{S}_n\)-invariant kernels ⋮ Toeplitz operators and Hilbert modules on the symmetrized polydisc ⋮ Finite Blaschke products and the construction of rational \(\Gamma\)-inner functions ⋮ Canonical decomposition of operators associated with the symmetrized polydisc ⋮ A certain rational function and operator theory on the symmetrized polydisc ⋮ The fundamental operator tuples associated with the symmetrized polydisc ⋮ Automorphisms and the fundamental operators associated with the symmetrized tridisc ⋮ Algebraic properties of Toeplitz operators on the symmetrized polydisk ⋮ Survey of last ten years of work done in India in some selected areas of functional analysis and operator theory ⋮ Structure theorems for operators associated with two domains related to \(\mu \)-synthesis ⋮ On \(\Gamma_n\)-contractions and their conditional dilations ⋮ Multiplication operators on the Bergman space by proper holomorphic mappings ⋮ A Schwarz lemma for two families of domains and complex geometry ⋮ Characterizations of the symmetrized polydisc via another family of domains

Cites Work

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• Dilations of \(\varGamma\)-contractions by solving operator equations
• The magic functions and automorphisms of a domain
• Polynomial convexity
• Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality
• Geometry of the symmetrized polydisc
• Reproducing kernel for a class of weighted Bergman spaces on the symmetrized polydisc
• Operator Theory on Symmetrized Bidisc
• Generalized Bergman Kernels and the Cowen-Douglas Theory
• Operators having the symmetrized bidisc as a spectral set
• A Generalization of a Theorem of Bôcher

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