Multiplication operators on the Bergman space via the Hardy space of the bidisk

DOI10.1515/CRELLE.2009.021zbMath1216.47055OpenAlexW2046391802MaRDI QIDQ3619636

Shun Hua Sun, Changyong Zhong, Kunyu Guo, DeChao Zheng

Publication date: 8 April 2009

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2009.021

Mathematics Subject Classification ID

Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Invariant subspaces of linear operators (47A15) Dilations, extensions, compressions of linear operators (47A20) Linear operators on function spaces (general) (47B38) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items (44)

Distinguished subspaces of Topelitz operators on N_ɸ-type quotient modules ⋮ Reducibility for a class of analytic multipliers on the Dirichlet space ⋮ Reducing subspaces of tensor products of weighted shifts ⋮ The core operator and the compressed multipliers on \(M_{\psi,\varphi}\)-type submodules ⋮ Hilbert-schmidtness of some finitely generated submodules in \(H^2(\mathbb{D}^2)\) ⋮ Reducing subspaces for a class of non-analytic Toeplitz operators on the bidisk ⋮ Reducing subspaces of multiplication operators on the Dirichlet space ⋮ Reducibility for a class of analytic multipliers on Sobolev disk algebra ⋮ A note on reducing subspaces of Toeplitz operator on the weighted analytic function spaces of the bidisk \(H_w^2 \left(\mathbb{D}^2\right)\) ⋮ Geometric constructions of thin Blaschke products and reducing subspace problem ⋮ Von Neumann algebras generated by multiplication operators on the weighted Bergman space: a function-theory view into operator theory ⋮ Restriction of Toeplitz operators on their reducing subspaces ⋮ Multiplication operators on the Bergman space via analytic continuation ⋮ Multiplication operators defined by twisted proper holomorphic maps on Bergman spaces ⋮ The pluriharmonic Hardy space and Toeplitz operators ⋮ Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces ⋮ Reducing subspaces of multiplication operators with the symbol \(\alpha z^k+\beta w^l\) on \(L_a^2 (\mathbb D^2)\) ⋮ Multiplication operators on Hardy and weighted Bergman spaces over planar regions ⋮ Commutants and complex symmetry of finite Blaschke product multiplication operator in ⋮ Hilbert-Schmidtness of Submodules in $H^2 (\mathbb{D}^2 )$ Containing $θ(z)−\varphi (w)$ ⋮ The commutant of some shift operators ⋮ The reducibility of truncated Toeplitz operators ⋮ On the double commutant of Cowen-Douglas operators ⋮ Reducibility and unitarily equivalence for a class of analytic multipliers on the Dirichlet space ⋮ Reducing subspaces for analytic multipliers of the Bergman space ⋮ Bundle shifts and Toeplitz operators on \(\mathcal{N}_{\psi}\)-type quotient modules of the tridisc ⋮ Multiplication operators defined by a class of polynomials on \({L_a^2(\mathbb{D}^2)}\) ⋮ Joint reducing subspaces of multiplication operators and weight of multi-variable Bergman spaces ⋮ Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk ⋮ Doubly commuting mixed invariant subspaces in the polydisc ⋮ Multiplication operators on the Bergman spaces of polygons ⋮ Reducing subspaces for a class of nonanalytic Toeplitz operators ⋮ Totally abelian Toeplitz operators and geometric invariants associated with their symbol curves ⋮ A note on unbounded generalized multiplication operators ⋮ Reducing subspaces of multiplication operators on function spaces ⋮ Reducing subspaces of analytic Toeplitz operators on the Bergman space of the annulus ⋮ Functional spectrum of contractions ⋮ Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk ⋮ Reducing subspaces of some multiplication operators on the Bergman space over polydisk ⋮ Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk ⋮ Reducing subspaces for a class of multiplication operators on the Dirichlet space ⋮ Generalized multiplication operators of higher order on weighted Hardy spaces ⋮ Multiplication operators on the Bergman space by proper holomorphic mappings ⋮ Beurling type theorem on the Bergman space via the Hardy space of the bidisk

Cites Work

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• Analytic functions of finite valence, with applications to Toeplitz operators
• Analytic functions sharing level curves and tracts
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• Beurling's theorem for the Bergman space
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• Reducing subspaces of analytic Toeplitz operators
• The core operator and congruent submodules
• Fredholm and Invertible n-Tuples of Operators. The Deformation Problem
• Hardy Space Expectation Operators and Reducing Subspaces
• The Commutant of a Class of Analytic Toeplitz Operators
• The Commutant of an Analytic Toeplitz Operator
• Reducing Subspaces for a Class of Multiplication Operators
• On a Class of Operators
• Complex geometry and operator theory
• Operator theory in the Hardy space over the bidisk. III
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