Displaying similar documents to “On self-commutators of Toeplitz operators with rational symbols”

Zero sums of products of Toeplitz and Hankel operators on the Hardy space

Young Joo Lee (2015)

Studia Mathematica

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On the Hardy space of the unit disk, we consider operators which are finite sums of products of a Toeplitz operator and a Hankel operator. We then give characterizations for such operators to be zero. Our results extend several known results using completely different arguments.

Projections onto the spaces of Toeplitz operators

Marek Ptak (2005)

Annales Polonici Mathematici

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Projections onto the spaces of all Toeplitz operators on the N-torus and the unit sphere are constructed. The constructions are also extended to generalized Toeplitz operators and applied to show hyperreflexivity results.

Positive Schatten class Toeplitz operators on the ball

Boo Rim Choe, Hyungwoon Koo, Young Joo Lee (2008)

Studia Mathematica

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On the harmonic Bergman space of the ball, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten class operator in terms of averaging functions and Berezin transforms.

The Berezin transform and operators on spaces of analytic functions

Karel Stroethoff (1997)

Banach Center Publications

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In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz...

Reflexivity of Toeplitz operators in multiply connected regions

Wojciech Młocek, Marek Ptak (2016)

Colloquium Mathematicae

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Subspaces of Toeplitz operators on the Hardy spaces over a multiply connected region in the complex plane are investigated. A universal covering map of such a region and the group of automorphisms invariant with respect to the covering map connect the Hardy space on this multiply connected region with a certain subspace of the classical Hardy space on the disc. We also present some connections of Toeplitz operators on both spaces from the reflexivity point of view.

Properties of two variables Toeplitz type operators

Elżbieta Król-Klimkowska, Marek Ptak (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.

On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane

Wojciech Młocek, Marek Ptak (2013)

Czechoslovak Mathematical Journal

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The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between L ∞ spaces on the unit circle and the...

Hölder functions in Bergman type spaces

Yingwei Chen, Guangbin Ren (2012)

Studia Mathematica

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It seems impossible to extend the boundary value theory of Hardy spaces to Bergman spaces since there is no boundary value for a function in a Bergman space in general. In this article we provide a new idea to show what is the correct version of Bergman spaces by demonstrating the extension to Bergman spaces of a result of Hardy-Littlewood in Hardy spaces, which characterizes the Hölder class of boundary values for a function from Hardy spaces in the unit disc in terms of the growth...