Product of H-Toeplitz operator and Toeplitz operator on the Bergman space

Ding, Qian; Chen, Yong

doi:10.3934/math.20231059

MATH

2023

DOI: 10.3934/math.20231059

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Product of H-Toeplitz operator and Toeplitz operator on the Bergman space

Qian Ding

Yong Chen

Abstract: <abstract>In this paper, we characterize when the product of two H-Toeplitz operators to be another H-Toeplitz with one general and another quasihomogeneous symbols. Also, we describe the product of H-Toeplitz operator and Toeplitz operator to be another H-Toeplitz with certain harmonic symbols.</abstract>

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Cited by 2 publications

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Commuting Toeplitz operators and H-Toeplitz operators on Bergman space

Ding

2023

MATH

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<abstract>In this paper, we consider the H-Toeplitz and Toeplitz operators acting on the Bergman space. First, we describe the characterizations of commutativity of two H-Toeplitz operators with certain harmonic symbols. For the general case, it seems very hard. As an extension to the study of Toeplitz operators on the Bergman space, we present the necessary and sufficient conditions of the commutativity of the H-Toeplitz operator and the Toeplitz operator with non-harmonic symbols.</abstract>

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Commuting Toeplitz operators and H-Toeplitz operators on Bergman space

Ding

2023

MATH

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H-Toeplitz operators on the Dirichlet type space

Huang,

Zhang

2024

MATH

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<abstract>In this paper, we conducted a study of H-Toeplitz operators on the Dirichlet type space $ \mathfrak{D}_{t} $, which included several aspects. To begin, we established the matrix representation of the H-Toeplitz operator $ S_{\varphi} $ with respect to the orthonormal basis of $ \mathfrak{D}_t $. Subsequently, we characterized the compactness of $ S_{\varphi} $ in terms of the symbol $ \varphi $. Furthermore, we developed a new method to investigate the algebraic properties of H-Toeplitz operators, including self-adjointness, diagonality, co-isometry, partial isometry as well as commutativity.</abstract>

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Product of H-Toeplitz operator and Toeplitz operator on the Bergman space

Cited by 2 publications

References 9 publications

Commuting Toeplitz operators and H-Toeplitz operators on Bergman space

Commuting Toeplitz operators and H-Toeplitz operators on Bergman space

H-Toeplitz operators on the Dirichlet type space

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