Beurling type theorem on the Bergman space via the Hardy space of the bidisk

DOI10.1007/s11425-009-0172-xzbMath1191.47007OpenAlexW2003419308MaRDI QIDQ1047873

DeChao Zheng, Shun Hua Sun

Publication date: 6 January 2010

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-009-0172-x

zbMATH Keywords

Hardy spaceBergman spaceinvariant subspacesBergman shift

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Bergman spaces and Fock spaces (30H20)

Related Items (15)

Random weighted shifts on Hilbert spaces of analytic functions ⋮ On Wold Type Decomposition for Closed Range Operators ⋮ The core operator and the compressed multipliers on \(M_{\psi,\varphi}\)-type submodules ⋮ 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 ⋮ Random weighted shifts ⋮ Hilbert-Schmidtness of Submodules in $H^2 (\mathbb{D}^2 )$ Containing $θ(z)−\varphi (w)$ ⋮ 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 ⋮ Quasi-wandering subspaces in the Bergman space ⋮ \(M_\varphi\)-type submodules over the bidisk ⋮ Wandering subspace property of the shift operator on a class of invariant subspaces of the weighted Bergman space \(L_a^2(dA_2)\) ⋮ Wold-type decomposition for some regular operators

Cites Work

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• Super-isometrically dilatable operators
• Invariant subspaces, dilation theory, and the structure of the predual of a dual algebra. I
• Beurling's theorem for the Bergman space
• Operator theory in the Hardy space over the bidisk. I
• Bergman-type reproducing kernels, contractive divisors, and dilations
• Wandering subspace theorems
• The core operator and congruent submodules
• On two problems concerning linear transformations in Hilbert space
• Wold-type decompositions and wandering subspaces for operators close to isometries
• Multiplication operators on the Bergman space via the Hardy space of the bidisk
• Higher order Hilbert-Schmidt Hankel forms and tensors of analytical kernels
• Operator theory in the Hardy space over the bidisk. III
• Operator theory in the Hardy space over the bidisk. II

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