Bergman-type reproducing kernels, contractive divisors, and dilations

DOI10.1006/jfan.2001.3874zbMath1038.46021OpenAlexW2069102260MaRDI QIDQ1604628

Scott A. McCullough, Stephan Richter

Publication date: 8 July 2002

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

Full work available at URL: https://doi.org/10.1006/jfan.2001.3874

zbMATH Keywords

Hilbert spacefactorization theoremsBergman-type kernelmultiplier invariant subspacesesquianalytic reproducing kernel

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) 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) Bergman spaces of functions in several complex variables (32A36) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

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An invariant subspace theorem and invariant subspaces of analytic reproducing kernel Hilbert spaces. II, An Introduction to Hilbert Module Approach to Multivariable Operator Theory, Weighted Bergman spaces: shift-invariant subspaces and input/state/output linear systems, The root operator on finite zero based invariant subspaces of the weighted Bergman space, Wandering subspaces and the Beurling type theorem. I, Wandering subspaces and quasi-wandering subspaces in the Hardy-Sobolev spaces, Finite zero-based invariant subspaces of the shift operator on reproducing kernel spaces, Dilations and operator models of \(\mathcal{W}\)-hypercontractions, Wandering subspaces and the Beurling type theorem. III, The wandering subspace property and Shimorin's condition of shift operator on the weighted Bergman spaces, Beurling type theorem on the Hilbert space generated by a positive sequence, The jumping operator on invariant subspaces in spaces of analytic functions, \(M_\varphi\)-type submodules over the bidisk, A Beurling–Lax–Halmos theorem for spaces with a complete Nevanlinna–Pick factor, Wandering subspace property of the shift operator on a class of invariant subspaces of the weighted Bergman space \(L_a^2(dA_2)\), Beurling type theorem on the Bergman space via the Hardy space of the bidisk, Analytic contractions, nontangential limits, and the index of invariant subspaces, Free outer functions in complete Pick spaces

Cites Work

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