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Complex Symmetric Toeplitz Operators on the Unit Polydisk and the Unit Ball

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Abstract

In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Nanchang Hangkong University, Nanchang, 330063, China

    Cao Jiang  (蒋操)

  2. School of Mathematics, Tianjin University, Tianjin, 300350, China

    Xingtang Dong  (董兴堂) & Zehua Zhou  (周泽华)

Authors
  1. Cao Jiang  (蒋操)
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  2. Xingtang Dong  (董兴堂)
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  3. Zehua Zhou  (周泽华)
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Corresponding author

Correspondence to Xingtang Dong  (董兴堂).

Additional information

This work was supported in part by the National Natural Science Foundation of China (11201331; 11771323).

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Jiang, C., Dong, X. & Zhou, Z. Complex Symmetric Toeplitz Operators on the Unit Polydisk and the Unit Ball. Acta Math Sci 40, 35–44 (2020). https://doi.org/10.1007/s10473-020-0103-2

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  • DOI: https://doi.org/10.1007/s10473-020-0103-2

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