Displaying similar documents to “Products of Toeplitz operators and Hankel operators”

On Pták’s generalization of Hankel operators

Carmen H. Mancera, Pedro José Paúl (2001)

Czechoslovak Mathematical Journal

Similarity:

In 1997 Pták defined generalized Hankel operators as follows: Given two contractions T 1 ∈ ℬ ( ℋ 1 ) and T 2 ∈ ℬ ( ℋ 2 ) , an operator X ℋ 1 → ℋ 2 is said to be a generalized Hankel operator if T 2 X = X T 1 * and X satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of T 1 and T 2 . This approach, call it (P), contrasts with a previous one developed by Pták and Vrbová in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong...

Properties of two variables Toeplitz type operators

Elżbieta Król-Klimkowska, Marek Ptak (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Similarity:

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.

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

Young Joo Lee (2015)

Studia Mathematica

Similarity:

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.

Asymmetric truncated Toeplitz operators equal to the zero operator

Joanna Jurasik, Bartosz Łanucha (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

Asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These operators are natural generalizations of truncated Toeplitz operators. In this paper we describe symbols of asymmetric truncated Toeplitz operators equal to the zero operator.

Deformation quantization and Borel's theorem in locally convex spaces

Miroslav Engliš, Jari Taskinen (2007)

Studia Mathematica

Similarity:

It is well known that one can often construct a star-product by expanding the product of two Toeplitz operators asymptotically into a series of other Toeplitz operators multiplied by increasing powers of the Planck constant h. This is the Berezin-Toeplitz quantization. We show that one can obtain in a similar way in fact any star-product which is equivalent to the Berezin-Toeplitz star-product, by using instead of Toeplitz operators other suitable mappings from compactly supported smooth...

Projections onto the spaces of Toeplitz operators

Marek Ptak (2005)

Annales Polonici Mathematici

Similarity:

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.

Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices

A.K. Abdikalykov, V.N. Chugunov, Kh.D. Ikramov (2015)

Special Matrices

Similarity:

Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.

On truncations of Hankel and Toeplitz operators.

Aline Bonami, Joaquim Bruna (1999)

Publicacions Matemàtiques

Similarity:

We study the boundedness properties of truncation operators acting on bounded Hankel (or Toeplitz) infinite matrices. A relation with the Lacey-Thiele theorem on the bilinear Hilbert transform is established. We also study the behaviour of the truncation operators when restricted to Hankel matrices in the Schatten classes.

Positive Schatten class Toeplitz operators on the ball

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

Studia Mathematica

Similarity:

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.