Reducing subspaces of non-analytic Toeplitz operators on weighted Hardy and Dirichlet spaces of the bidisk

DOI10.1016/j.jmaa.2017.11.004zbMath1493.47039OpenAlexW2769176123MaRDI QIDQ1684807

Caixing Gu

Publication date: 12 December 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.11.004

zbMATH Keywords

reducing subspacescommutant of a von Neumann algebranon-analytic Toeplitz operatorsweighted Dirichlet space of the bidiskweighted Hardy space of the bidisk

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) (H^p)-spaces (42B30) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35)

Related Items (8)

DECOMPOSITION OF THE KRONECKER SUMS OF MATRICES INTO A DIRECT SUM OF IRREDUCIBLE MATRICES ⋮ Reducing subspaces for Toeplitz operator \(T_{z_1^{k_1} z_2^{k_2} + a\overline{z}_1^{l_1}\overline{z}_2^{l_2}}\) on the weighted Hardy space over the bidisk ⋮ Multiplication operators defined by twisted proper holomorphic maps on Bergman spaces ⋮ On quasi-affinity and reducing subspaces of multiplication operator on a certain closed subspace ⋮ Unnamed Item ⋮ Reducing subspaces for the product of a forward and a backward operator-weighted shifts ⋮ The operator \(M_{z_1^n z_2^n}\) on subspaces of Bergman spaces over the biannulus ⋮ Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk

Cites Work

• Reducing subspaces of tensor products of weighted shifts
• Reducing subspaces for a class of non-analytic Toeplitz operators on the bidisk
• Reducing subspaces of multiplication operators on the Dirichlet space
• Reducing subspaces for analytic multipliers of the Bergman space
• Multiplication operators defined by a class of polynomials on \({L_a^2(\mathbb{D}^2)}\)
• Multiplication operators on the Bergman space via analytic continuation
• Reducing subspaces of multiplication operators with the symbol \(\alpha z^k+\beta w^l\) on \(L_a^2 (\mathbb D^2)\)
• Möbius-invariant Hilbert spaces in polydiscs
• Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces
• \(m\)-isometric transformations of Hilbert space. I
• On \((m, p)\)-expansive and \((m, p)\)-contractive operators on Hilbert and Banach spaces
• Multiplication operators on the Bergman space
• The \((m,q)\)-isometric weighted shifts on \(l_{p}\) spaces
• REDUCING SUBSPACES OF WEIGHTED SHIFTS WITH OPERATOR WEIGHTS
• REDUCING SUBSPACES FOR TOEPLITZ OPERATORS ON THE POLYDISK
• REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISK
• Cyclic Vectors in the Dirichlet Space
• A Representation Theorem for Cyclic Analytic Two-Isometries
• Reducing subspaces of weighted shift operators
• Reducing Subspaces for a Class of Multiplication Operators
• Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk
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