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Commuting and Semi-commuting Monomial-type Toeplitz Operators on Some Weakly Pseudoconvex Domains

Part of: Special classes of linear operators Holomorphic functions of several complex variables

Published online by Cambridge University Press:  09 January 2019

Cao Jiang ,
Xing-Tang Dong  and
Ze-Hua Zhou
Cao Jiang
Affiliation:
School of Mathematics, Tianjin University, Tianjin, 300354, P.R. China Email: jiangcc96@163.comdongxingtang@163.comzehuazhoumath@aliyun.com
Xing-Tang Dong
Affiliation:
School of Mathematics, Tianjin University, Tianjin, 300354, P.R. China Email: jiangcc96@163.comdongxingtang@163.comzehuazhoumath@aliyun.com
Ze-Hua Zhou
Affiliation:
School of Mathematics, Tianjin University, Tianjin, 300354, P.R. China Email: jiangcc96@163.comdongxingtang@163.comzehuazhoumath@aliyun.com
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Abstract

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In this paper, we completely characterize the finite rank commutator and semi-commutator of two monomial-type Toeplitz operators on the Bergman space of certain weakly pseudoconvex domains. Somewhat surprisingly, there are not only plenty of commuting monomial-type Toeplitz operators but also non-trivial semi-commuting monomial-type Toeplitz operators. Our results are new even for the unit ball.

Keywords

Toeplitz operatorBergman spacemonomial-type symbolweakly pseudoconvex domain

MSC classification

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Secondary: 32A36: Bergman spaces
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 2 , June 2019 , pp. 327 - 340
Copyright
© Canadian Mathematical Society 2018 

Footnotes

Z.-H. Zhou is corresponding author. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11201331; 11371276; 11771323).

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