On Beurling-type theorems in weighted 𝑙² and Bergman spaces

DOI10.1090/S0002-9939-02-06721-7zbMath1046.47024MaRDI QIDQ4794577

Serguei Shimorin

Publication date: 19 February 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Bergman spaceswandering subspacesanalytic operators

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Invariant subspaces of linear operators (47A15) Spaces of bounded analytic functions of one complex variable (30H05) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37)

Related Items (24)

Multivariable Beurling–Lax representations: the commutative and free noncommutative settings ⋮ Poisson integrals for standard weighted Laplacians in the unit disc ⋮ Weighted Bergman spaces: shift-invariant subspaces and input/state/output linear systems ⋮ Dilations, wandering subspaces, and inner functions ⋮ A Beurling type theorem in weighted Bergman spaces ⋮ Several properties of \(\alpha \)-harmonic functions in the unit disk ⋮ Finite zero-based invariant subspaces of the shift operator on reproducing kernel spaces ⋮ Random weighted shifts ⋮ Tridiagonal kernels and left-invertible operators with applications to Aluthge transforms ⋮ Beurling’s phenomenon on analytic Hilbert spaces over the complex plane ⋮ Wandering subspace property for homogeneous invariant subspaces ⋮ Noncommutative hyperballs, wandering subspaces, and inner functions ⋮ The wandering subspace property and Shimorin's condition of shift operator on the weighted Bergman spaces ⋮ A characteristic operator function for the class of \(n\)-hypercontractions ⋮ Invariant subspaces and operator model theory on noncommutative varieties ⋮ Operator-valued Bergman inner functions as transfer functions ⋮ \(M_\varphi\)-type submodules over the bidisk ⋮ Critical structures of inner functions ⋮ A Beurling–Lax–Halmos theorem for spaces with a complete Nevanlinna–Pick factor ⋮ A trace formula on invariant subspaces of Hardy space induced by rotation-invariant Borel measure ⋮ An expansive multiplier property for operator-valued Bergman inner functions ⋮ Extremal functions in weighted Bergman spaces ⋮ Wandering subspace property of the shift operator on a class of invariant subspaces of the weighted Bergman space \(L_a^2(dA_2)\) ⋮ Mean value surfaces with prescribed curvature form

Cites Work

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• Beurling's theorem for the Bergman space
• Approximate spectral synthesis in the Bergman space
• Wold-type decompositions and wandering subspaces for operators close to isometries
• Invariant subspaces of the Dirichlet shift.
• On the failure of optimal factorization for certain weighted bergman spaces
• Theory of Reproducing Kernels

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