Pure inner functions, distinguished varieties and toral algebraic commutative contractive pairs

DOI10.1090/proc/16590MaRDI QIDQ6154326

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Publication date: 15 February 2024

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

zbMATH Keywords

inner functionsdistinguished varietiestoral algebraic pairs

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Dilations, extensions, compressions of linear operators (47A20) Analytic subsets and submanifolds (32C25) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)

Cites Work

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• Ando dilations, von Neumann inequality, and distinguished varieties
• Representation and index theory for \(C^*\)-algebras generated by commuting isometries
• A classification of \(n\)-tuples of commuting shifts of finite multiplicity
• Rational dilation problems associated with constrained algebras
• Factorizations of contractions
• Distinguished varieties through the Berger-Coburn-Lebow theorem
• The joint spectrum for a commuting pair of isometries in certain cases
• Inner functions on the bidisk and associated Hilbert spaces
• Distinguished varieties
• Toral algebraic sets and function theory on polydisks
• Harmonic analysis of operators on Hilbert space
• Canonical Models for Bi-isometries
• Dilations and constrained algebras
• Polynomials defining distinguished varieties
• Algebraic pairs of isometries
• On polynomial $n$-tuples of commuting isometries
• Numerical invariants for commuting isometric pairs
• Maximum theorems for vector valued holomorphic functions

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