Properties of Beurling-type submodules via Agler decompositions

DOI10.1016/j.jfa.2016.10.007zbMath1417.47004arXiv1411.5759OpenAlexW2240475375MaRDI QIDQ333114

Constanze Liaw, Kelly Bickel

Publication date: 9 November 2016

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

Full work available at URL: https://arxiv.org/abs/1411.5759

zbMATH Keywords

essential normalityAgler decompositioncompressed shiftstwo-variable model spaces

Mathematics Subject Classification ID

Problem books (00A07) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Dilations, extensions, compressions of linear operators (47A20) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items

Distinguished subspaces of Topelitz operators on N_ɸ-type quotient modules, Essential normality for Beurling-type quotient modules over tube-type domains, The core operator and the compressed multipliers on \(M_{\psi,\varphi}\)-type submodules, The Agler reducing subspace for the operator-valued inner function over the bidisk, Beurling quotient subspaces for covariant representations of product systems, Properties of vector-valued submodules on the bidisk, A geometric approach to the compressed shift operator on the Hardy space over the bidisk, Pairs of inner projections and two applications, Schur functions and inner functions on the bidisc, Beurling quotient modules on the polydisc, The reducibility of compressed shifts on a class of quotient modules over the bidisk, Level curve portraits of rational inner functions, The reducibility of compressed shifts on Beurling type quotient modules over the bidisk, Properties of compressed shifts on Beurling type quotient module of Hardy space over the bidisk

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Clark model in the general situation
• Rational inner functions in the Schur-Agler class of the polydisk
• A Carathéodory theorem for the bidisk via Hilbert space methods
• Rank-one commutators on invariant subspaces of the Hardy space on the bidisk
• A general Christoffel-Darboux type formula
• Beurling type quotient modules over the bidisk and boundary representations
• Unitary colligations, reproducing kernel Hilbert spaces, and Nevanlinna-Pick interpolation in several variables
• Operator theory in the Hardy space over the bidisk. I
• Backward shift invariant subspaces in the bidisc
• Equivalence of quotient Hilbert modules
• Operator monotone functions and Löwner functions of several variables
• Fundamental Agler decompositions
• Inner functions on the bidisk and associated Hilbert spaces
• Scattering systems with several evolutions and multidimensional input/state/output systems
• Distinguished varieties
• On the spectra of operators on tensor products
• Harmonic analysis of operators on Hilbert space
• Recent Progress on Truncated Toeplitz Operators
• What Hilbert spaces can tell us about bounded functions on the bidisk
• The Validity of Beurling Theorems in Polydiscs
• INTERPOLATING SEQUENCES ON THE BIDISK
• A Schwarz lemma on the polydisk
• Properties of vector-valued submodules on the bidisk
• A geometric approach to finite rank unitary perturbations
• Equivalence of quotient Hilbert modules–II
• Operator theory in the Hardy space over the bidisk. III
• Operator theory in the Hardy space over the bidisk. II