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.
Citation: Peiying Huang, Yiyuan Zhang. H-Toeplitz operators on the Dirichlet type space[J]. AIMS Mathematics, 2024, 9(7): 17847-17870. doi: 10.3934/math.2024868
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.
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Peiying Huang, Yiyuan Zhang. H-Toeplitz operators on the Dirichlet type space[J]. AIMS Mathematics, 2024, 9(7): 17847-17870. doi: 10.3934/math.2024868
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