On some Bergman shift operators

DOI10.1007/s11785-010-0101-6zbMath1273.47046OpenAlexW2118837823MaRDI QIDQ371717

Olof Giselsson, Anders Olofsson

Publication date: 10 October 2013

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-010-0101-6

zbMATH Keywords

invariant subspace\(n\)-isometryWold decompositionBergman shift operator

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items

Weighted Bergman spaces: shift-invariant subspaces and input/state/output linear systems ⋮ Multivariable Bergman shifts and Wold decompositions ⋮ Factorizations of kernels and reproducing kernel Hilbert spaces ⋮ Interpolation in Sub-Bergman Spaces

Cites Work

• Doubly-invariant subspaces for the shift on the vector-valued Sobolev spaces of the disc and annulus
• The Arveson extension theorem and coanalytic models
• Beurling's theorem for the Bergman space
• Wandering subspace theorems
• \(m\)-isometric transformations of Hilbert space. I
• \(m\)-isometric transformations of Hilbert space. II
• \(m\)-isometric transformations of Hilbert space. III
• An operator-valued Berezin transform and the class of \(n\)-hypercontractions
• A characteristic operator function for the class of \(n\)-hypercontractions
• Wold-type decompositions and wandering subspaces for operators close to isometries
• Shifts on Hilbert spaces.
• Characterizations of Bergman space Toeplitz operators with harmonic symbols
• Invariant subspaces of the Dirichlet shift.
• A biharmonic maximum principle for hyperbolic surfaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item