Dilations and constrained algebras

DOI10.7153/OAM-10-48zbMath1387.47008arXiv1305.4272OpenAlexW2962794879WikidataQ57451927 ScholiaQ57451927MaRDI QIDQ2954254

Michael A. Dritschel, Michael T. Jury, Scott A. McCullough

Publication date: 12 January 2017

Published in: Operators and Matrices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.4272

zbMATH Keywords

dilationsrealizationsinner functionsNevanlinna-Pick interpolationcompletely contractive representationsHerglotz representations

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) Operator spaces and completely bounded maps (46L07) Dilations, extensions, compressions of linear operators (47A20) Moment problems and interpolation problems in the complex plane (30E05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Spectral sets of linear operators (47A25) Rings and algebras of continuous, differentiable or analytic functions (46E25) Representations of (nonselfadjoint) operator algebras (47L55) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48) Kernel functions in one complex variable and applications (30C40)

Related Items (4)

Distinguished varieties through the Berger-Coburn-Lebow theorem ⋮ Rational dilation problems associated with constrained algebras ⋮ Pure inner functions, distinguished varieties and toral algebraic commutative contractive pairs ⋮ Operator algebras of higher rank numerical semigroups

Cites Work

• On an inequality of von Neumann and an application of the metric theory of tensor products to operators theory. (Appendix by S. Kaijser and N. Th. Varopoulos.)
• Eigenvalues of Toeplitz operators on the annulus and Neil algebra
• Unitary dilations for commuting contractions
• Test functions in constrained interpolation
• Polynomials defining distinguished varieties
• The failure of rational dilation on a triply connected domain
• Pairs of Inner Functions on Finite Riemann Surfaces

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