Spectral sets and distinguished varieties in the symmetrized bidisc

DOI10.1016/j.jfa.2013.12.022zbMath1311.47008arXiv1310.2769OpenAlexW2963124573MaRDI QIDQ2511675

Sourav Pal, Orr Moshe Shalit

Publication date: 6 August 2014

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

Full work available at URL: https://arxiv.org/abs/1310.2769

zbMATH Keywords

spectral setvon Neumann's inequalitydistinguished varietiessymmetrized bidiscfundamental operatorcomplete spectral set

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Dilations, extensions, compressions of linear operators (47A20) Canonical models for contractions and nonselfadjoint linear operators (47A45) Spectral sets of linear operators (47A25)

Related Items (21)

Dilation, functional model and a complete unitary invariant for C.0Γn-contractions ⋮ Distinguished varieties through the Berger-Coburn-Lebow theorem ⋮ A Schwarz lemma for the symmetrized polydisc via estimates on another family of domains ⋮ Finite Blaschke products and the construction of rational \(\Gamma\)-inner functions ⋮ Essentially normal quotient weighted Bergman modules over the bidisk and distinguished varieties ⋮ Determining sets for holomorphic functions on the symmetrized bidisk ⋮ The symmetrization map and \(\Gamma\)-contractions ⋮ The complex geometry of a domain related to \(\mu\)-synthesis ⋮ Dilation theory: a guided tour ⋮ Ando dilations, von Neumann inequality, and distinguished varieties ⋮ A generalized Schwarz lemma for two domains related to \(\mu\)-synthesis ⋮ 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 ⋮ 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 ⋮ A Schwarz lemma for two families of domains and complex geometry ⋮ Characterizations of the symmetrized polydisc via another family of domains ⋮ Level curve portraits of rational inner functions ⋮ A model theory for operators associated with a domain related to \(\mu\)-synthesis

Cites Work

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• Distinguished varieties
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• Polynomials defining distinguished varieties
• A Schwarz Lemma for the Symmetrized Bidisc
• Operators having the symmetrized bidisc as a spectral set
• Unitary 𝑁-dilations for tuples of commuting matrices
• Extremal holomorphic maps and the symmetrized bidisc
• The failure of rational dilation on a triply connected domain
• Classical function theory, operator dilation theory, and machine computation on multiply-connected domains

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