Abstract
In this paper, we investigate the complex symmetric structure of Toeplitz operators Tϕ on the Hardy space over the bidisk. We first characterize the weighted composition operators, Wu, v which are \({\cal J}\)-symmetric and unitary. As a consequence, we characterize conjugations of the form Au, v. In addition, a class of conjugations of the form Cλ, a is introduced. We show that the class of conjugations Cλ, a coincides with the class of conjugations Au, v; we then characterize the complex symmetry of the Toeplitz operators Tϕ with respect to the conjugation Cλ, a.
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Acknowledgements
The second author would like to thank Professor Chen Yong from Hangzhou Normal University for helpful discussions during the process of completing the paper.
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The authors declare no conflict of interest.
Wang and Han’s research was partially supported by the National Natural Science Foundation of China (11771340, 12101179, 12171373).
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Wang, M., Wu, Q. & Han, K. Complex Symmetry of Toeplitz Operators over the Bidisk. Acta Math Sci 43, 1537–1546 (2023). https://doi.org/10.1007/s10473-023-0405-z
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DOI: https://doi.org/10.1007/s10473-023-0405-z