COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

doi:10.1007/s10473-020-103-2

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (1): 35-44.doi: 10.1007/s10473-020-103-2

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COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

Cao JIANG¹, Xingtang DONG², Zehua ZHOU²

1. School of Mathematics and Information Sciences, Nanchang Hangkong University, Nanchang 330063, China;
2. School of Mathematics, Tianjin University, Tianjin 300350, China

Received:2019-03-12 Revised:2019-05-08 Online:2020-02-25 Published:2020-04-14
Contact: Xingtang dong E-mail:dongxingtang@163.com,dongxingtang@tju.edu.cn
Supported by:
This work was supported in part by the National Natural Science Foundation of China (11201331; 11771323).

Abstract

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.

Key words: complex symmetric operator, Toeplitz operator, Bergman space, pluriharmonic Bergman space

CLC Number:

47B35

Cao JIANG, Xingtang DONG, Zehua ZHOU. COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL[J].Acta mathematica scientia,Series B, 2020, 40(1): 35-44.

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COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

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