COMPLEX SYMMETRY OF TOEPLITZ OPERATORS OVER THE BIDISK∗

COMPLEX SYMMETRY OF TOEPLITZ OPERATORS OVER THE BIDISK^∗

COMPLEX SYMMETRY OF TOEPLITZ OPERATORS OVER THE BIDISK^∗

COMPLEX SYMMETRY OF TOEPLITZ OPERATORS OVER THE BIDISK^∗

COMPLEX SYMMETRY OF TOEPLITZ OPERATORS OVER THE BIDISK^∗

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doi:10.1007/s10473-023-0405-z

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (4): 1537-1546.doi: 10.1007/s10473-023-0405-z

Maofa Wang¹, Qi Wu¹, Kaikai Han²

1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
2. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China

收稿日期:2022-03-11 修回日期:2022-08-29 发布日期:2023-08-08
作者简介:Maofa Wang, E-mail: mfwang.math@whu.edu.cn; Qi Wu, E-mail: whuqwu@whu.edu.cn; Kaikai Han, E-mail: kkhan.math@whu.edu.cn
基金资助:
*Wang and Han's research was partially supported by the National Natural Science Foundation of China (11771340, 12101179, 12171373).

Maofa Wang¹, Qi Wu¹, Kaikai Han²

1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
2. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China

Received:2022-03-11 Revised:2022-08-29 Published:2023-08-08
About author:Maofa Wang, E-mail: mfwang.math@whu.edu.cn; Qi Wu, E-mail: whuqwu@whu.edu.cn; Kaikai Han, E-mail: kkhan.math@whu.edu.cn
Supported by:
*Wang and Han's research was partially supported by the National Natural Science Foundation of China (11771340, 12101179, 12171373).

摘要： In this paper, we investigate the complex symmetric structure of Toeplitz operators $T_\phi$ on the Hardy space over the bidisk. We first characterize the weighted composition operators, $W_{u,v}$ which are $\mathcal{J}$ -symmetric and unitary. As a consequence, we characterize conjugations of the form $A_{u,v}$ . In addition, a class of conjugations of the form $C_{\lambda, a}$ is introduced. We show that the class of conjugations $C_{\lambda, a}$ coincides with the class of conjugations $A_{u,v}$ ; we then characterize the complex symmetry of the Toeplitz operators $T_\phi$ with respect to the conjugation $C_{\lambda, a}$ .

关键词: Toeplitz operators, Hardy space, complex symmetry

Abstract: In this paper, we investigate the complex symmetric structure of Toeplitz operators $T_\phi$ on the Hardy space over the bidisk. We first characterize the weighted composition operators, $W_{u,v}$ which are $\mathcal{J}$ -symmetric and unitary. As a consequence, we characterize conjugations of the form $A_{u,v}$ . In addition, a class of conjugations of the form $C_{\lambda, a}$ is introduced. We show that the class of conjugations $C_{\lambda, a}$ coincides with the class of conjugations $A_{u,v}$ ; we then characterize the complex symmetry of the Toeplitz operators $T_\phi$ with respect to the conjugation $C_{\lambda, a}$ .

Key words: Toeplitz operators, Hardy space, complex symmetry

Maofa Wang, Qi Wu, Kaikai Han. COMPLEX SYMMETRY OF TOEPLITZ OPERATORS OVER THE BIDISK^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1537-1546.

Maofa Wang, Qi Wu, Kaikai Han. COMPLEX SYMMETRY OF TOEPLITZ OPERATORS OVER THE BIDISK^∗[J]. Acta mathematica scientia,Series B, 2023, 43(4): 1537-1546.

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