Operator-valued Nevanlinna-Pick kernels and the functional models for contraction operators

DOI10.1007/BF01199793zbMath0621.47012OpenAlexW2009132678MaRDI QIDQ1089881

Thomas L. III. Kriete, Joseph A. Ball

Publication date: 1987

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01199793

zbMATH Keywords

commutant lifting theoremde Branges-Rovnyak model spaceHilbert space of vector-valued analytic functions with reproducing kernelmaximal factorable minorantoperator-valued Nevanlinna-Pick kernelsouter factorSz.-Nagy-Foias model space

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Canonical models for contractions and nonselfadjoint linear operators (47A45)

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On function and operator modules ⋮ Operator ranges and non-cyclic vectors for the backward shift ⋮ de Branges–Rovnyak Spaces: Basics and Theory ⋮ An Introduction to Hilbert Module Approach to Multivariable Operator Theory ⋮ Backward shift invariant operator ranges ⋮ Nonextreme de Branges-Rovnyak spaces as models for contractions ⋮ Which de Branges-Rovnyak spaces are Dirichlet spaces (and vice versa)? ⋮ Clark theory in the Drury-Arveson space ⋮ A construction of Krein spaces of analytic functions ⋮ The de Branges-Rovnyak Model ⋮ Multivariable backward-shift-invariant subspaces and observability operators ⋮ The De Branges-Rovnyak Model with Finite-Dimensional Coefficients ⋮ Aleksandrov-Clark theory for Drury-Arveson space ⋮ Noncommutative reproducing kernel Hilbert spaces ⋮ A note on common range of a class of co-analytic Toeplitz operators ⋮ On certain Riesz families in vector-valued de Branges-Rovnyak spaces ⋮ On spectrally associated Schur functions, Arov-inner functions and a Nehari-type completion problem for Schur functions ⋮ De Branges-Rovnyak realizations of operator-valued Schur functions on the complex right half-plane

Cites Work

• A corona theorem for countably many functions
• Interpolation problems in nest algebras
• Models for noncontractions
• Invariant subspaces and extremum problems in spaces of vector-valued functions
• Canonical models and the self-adjoint parts of dissipative operators
• On operator ranges
• Similarity of canonical models
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