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Complex Symmetric Toeplitz Operators

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Abstract

This paper aims to study when a Toeplitz operator \(T_\varphi \) on the Hardy space \(H^2\) of the unit disk is complex symmetric, that is, \(T_\varphi \) admits a symmetric matrix representation relative to some orthonormal basis of \(H^2\). For certain trigonometric symbols \(\varphi \), we give necessary and sufficient conditions for \(T_\varphi \) to be complex symmetric. In particular, we show that their complex symmetry coincides with the property “unitary equivalence to their transposes”.

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Acknowledgements

The authors wish to thank Prof. Yanyue Shi for many helpful discussions and the referees for many helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Qinggang Bu & Sen Zhu

  2. Department of Mathematics, Hangzhou Normal University, Hangzhou, 311121, People’s Republic of China

    Yong Chen

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  1. Qinggang Bu
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  2. Yong Chen
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  3. Sen Zhu
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Correspondence to Yong Chen.

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The second author was supported by NSFC (11771401) and the third author was supported by NSFC (11671167).

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Bu, Q., Chen, Y. & Zhu, S. Complex Symmetric Toeplitz Operators. Integr. Equ. Oper. Theory 93, 15 (2021). https://doi.org/10.1007/s00020-021-02629-5

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