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A Remark on Hyponormality of Block Toeplitz Operators on the Weighted Bergman Spaces

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Abstract

In this paper, we discuss block Toeplitz operators \(T_{\Phi }\) whose symbols are in the class of normal functions \(\Phi (z)= G^*(z)+F(z)\), where

$$\begin{aligned} F(z)= A_mz^m +A_Nz^N \quad \text {and}\quad G(z)=A_{-m}z^m + A_{-N}z^N \ (A_i\in M_2), \end{aligned}$$

on the weighted Bergman space. Additionally, we present a necessary and sufficient condition for the hyponormality of the block Toeplitz operators \(T_{\Phi }\).

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Acknowledgements

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Funding

This work was supported by the National Research Foundation of Korea(NRF) funded by the Korea government(MSIT)(No. 2021R1C1C1008713).

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  1. Department of Mathematics, Sungkyunkwan University, Suwon, 16419, Korea

    Jongrak Lee

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  1. Jongrak Lee
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Lee, J. A Remark on Hyponormality of Block Toeplitz Operators on the Weighted Bergman Spaces. Complex Anal. Oper. Theory 17, 78 (2023). https://doi.org/10.1007/s11785-023-01381-5

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