An analytic Toeplitz operator that commutes with a compact operator and a related class of Toeplitz operators

DOI10.1016/0022-1236(80)90098-1zbMath0438.47029OpenAlexW2116768493MaRDI QIDQ1141889

Carl C. Cowen

Publication date: 1980

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(80)90098-1

zbMATH Keywords

extensioncommutantanalytic Toeplitz operatorsecond commutant

Mathematics Subject Classification ID

Related Items (29)

An introduction to Rota's universal operators: properties, old and new examples and future issues ⋮ Rota's universal operators and invariant subspaces in Hilbert spaces ⋮ Composition operators on Hardy space in several complex variables ⋮ Multiplication by a finite Blaschke product on weighted Bergman spaces: commutant and reducing subspaces ⋮ Eigenmatrices and operators commuting with finite-rank operators ⋮ Von Neumann algebras generated by multiplication operators on the weighted Bergman space: a function-theory view into operator theory ⋮ Centralizers of Toeplitz operators with polynomial symbols ⋮ Hermitian weighted composition operators and Bergman extremal functions ⋮ Multiplication operators defined by twisted proper holomorphic maps on Bergman spaces ⋮ Reducing subspaces of multiplication operators with the symbol \(\alpha z^k+\beta w^l\) on \(L_a^2 (\mathbb D^2)\) ⋮ Normality properties of weighted composition operators on 𝐻² ⋮ Products of composition and analytic Toeplitz operators ⋮ Multiplication operators on Hardy and weighted Bergman spaces over planar regions ⋮ An operator not satisfying Lomonosov's hypothesis ⋮ Multiplication operators defined by covering maps on the Bergman space: the connection between operator theory and von Neumann algebras ⋮ Self-adjoint, unitary, and normal weighted composition operators in several variables ⋮ Weighted composition operators between different Fock spaces ⋮ 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 ⋮ Consequences of universality among Toeplitz operators ⋮ Operators $\alpha $-commuting with a compact operator ⋮ Reducing subspaces of multiplication operators on function spaces ⋮ Invariant subspaces of operator algebras ⋮ Hermitian weighted composition operators on $H^{2}$ ⋮ Asymptotics and isometries of weighted composition operators on Banach spaces of holomorphic functions ⋮ Convex-cyclic weighted composition operators and their adjoints ⋮ Does a typical ℓ_{𝑝}-space contraction have a non-trivial invariant subspace? ⋮ Normal and isometric weighted composition operators on the Fock space ⋮ A hyperbolic universal operator commuting with a compact operator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An operator not satisfying Lomonosov's hypothesis
• Isometries induced by composition operators and invariant subspaces
• Subordinate \(H^ P\) functions
• Reducing subspaces of analytic Toeplitz operators
• Subnormal operators
• Hardy Space Expectation Operators and Reducing Subspaces
• Analytic Toeplitz Operators with Automorphic Symbol
• The Commutants of Certain Analytic Toeplitz Operators
• Analytic Toeplitz Operators with Automorphic Symbol.II
• Lifting the Commutant of a Subnormal Operator
• The Commutant of a Class of Analytic Toeplitz Operators
• The Commutant of an Analytic Toeplitz Operator
• The Commutant of Analytic Toeplitz Operators
• Spectral Theory of Generalized Toeplitz Operators
• Bounded Holomorphic Functions on Finite Riemann Surfaces
• Composition Operators
• On Some Interpolation Problems for Analytic Functions

This page was built for publication: An analytic Toeplitz operator that commutes with a compact operator and a related class of Toeplitz operators