Interpolation in semigroupoid algebras

DOI10.1515/CRELLE.2007.033zbMath1139.47014arXivmath/0507083OpenAlexW2083270039WikidataQ57451935 ScholiaQ57451935MaRDI QIDQ5421658

Michael A. Dritschel, Stefania A. M. Marcantognini, Scott A. McCullough

Publication date: 24 October 2007

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507083

zbMATH Keywords

reproducing kernel Hilbert spacesgraph \(C^*\)-algebrasSchur-Agler classAgler-Pick interpolation

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Linear operator methods in interpolation, moment and extension problems (47A57) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)

Related Items (9)

The Use of Kernel Functions in Solving the Pick Interpolation Problem ⋮ Realization of functions on the symmetrized bidisc ⋮ Test functions, Schur-Agler classes and transfer-function realizations: the matrix-valued setting ⋮ Universal commutative operator algebras and transfer function realizations of polynomials ⋮ Determining sets for holomorphic functions on the symmetrized bidisk ⋮ Interpolating sequences for the Banach algebras generated by a class of test functions ⋮ Agler-commutant lifting on an annulus ⋮ Aperiodicity and cofinality for finitely aligned higher-rank graphs ⋮ Multivariable Generalizations of the Schur Class: Positive Kernel Characterization and Transfer Function Realization

Cites Work

• Bounded real lemma for structured noncommutative multidimensional linear systems and robust control
• The Pick interpolation theorem for finitely connected domains
• Caratheodory interpolation kernels
• Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras
• Interpolation problems in several variables
• Subalgebras of \(C^*\)-algebras. III: Multivariable operator theory
• Commutant lifting on a two holded domain
• On an intertwining lifting theorem for certain reproducing kernel Hilbert spaces
• Carathéodory Fejér interpolation in the ball with mixed derivatives
• Realization and interpolation for Schur--Agler-class functions on domains with matrix polynomial defining function in \(\mathbb C^{n}\)
• Multi-analytic operators on Fock spaces
• Nevanlinna-Pick type interpolation in a dual algebra
• Reproducing kernels for Hardy spaces on multiply connected domains
• Noncommutative interpolation and Poisson transforms
• Carathéodory interpolation on the non-commutative polydisk
• A commutant lifting theorem on the polydisc
• The failure of rational dilation on a triply connected domain
• Remarks on the operator-valued interpolation for multivariable bounded analytic functions
• Isometric representations of some quotients of \(H^\infty\) of an annulus

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