Wandering subspaces of the Bergman space and the Dirichlet space over \({{\mathbb{D}^{n}}}\)

DOI10.1007/s00020-014-2128-yzbMath1328.47010arXiv1306.0724OpenAlexW202330230MaRDI QIDQ464270

J. Herrera, D. Rodríguez-Gómez

Publication date: 17 October 2014

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.0724

zbMATH Keywords

Hardy spaceBergman spaceinvariant subspaceDirichlet spaceBeurling's theoremdoubly commuting invariant subspace

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Invariant subspaces of linear operators (47A15) Dilations, extensions, compressions of linear operators (47A20) Linear spaces and algebras of operators (47L99)

Related Items (7)

An Introduction to Hilbert Module Approach to Multivariable Operator Theory ⋮ Commutant of multiplication operators in weighted Bergman spaces on polydisk ⋮ Tensor product of quotient Hilbert modules ⋮ Rudin's submodules of \(H^2(\mathbb{D}^2)\) ⋮ Doubly commuting invariant subspaces for representations of product systems of \(C^*\)-correspondences ⋮ Cyclic polynomials in anisotropic Dirichlet spaces ⋮ Generating wandering subspaces for doubly commuting covariant representations

Cites Work

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• Beurling's theorem for the Bergman space
• On two problems concerning linear transformations in Hilbert space
• Wold-type decompositions and wandering subspaces for operators close to isometries
• Doubly commuting submodules of the Hardy module over polydiscs
• Shifts on Hilbert spaces.
• Invariant subspaces in Bergman space over the bidisc
• Invariant subspaces of the Dirichlet shift.
• The Validity of Beurling Theorems in Polydiscs
• Theory of Reproducing Kernels

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