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Commutators and Semi-commutators of Toeplitz Operators on the Unit Ball

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Abstract

Monomial Toeplitz operators on the Bergman space and the pluriharmonic Bergman space of the unit ball in \({\mathbb C}^n\) are natural generalizations of the classical unilateral and bilateral shift operators, respectively. In this paper we completely characterize when the commutator and semi-commutator of two monomial Toeplitz operators on the unit ball have finite rank.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin University, Tianjin, 300354, China

    Xing-Tang Dong

  2. Department of Mathematics, Shantou University, Guangdong, 515063, China

    Kehe Zhu

Authors
  1. Xing-Tang Dong
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  2. Kehe Zhu
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Correspondence to Kehe Zhu.

Additional information

Dong was supported in part by the National Natural Science Foundation of China (Grant No. 11201331). Zhu was partially supported by the China National Natural Science Foundation (Grant Number 11371234) and the Project of International Science and Technology Cooperation Innovation Platform in Universities in Guangdong Province (Grant Number 2014KGJHZ007).

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Dong, XT., Zhu, K. Commutators and Semi-commutators of Toeplitz Operators on the Unit Ball. Integr. Equ. Oper. Theory 86, 271–300 (2016). https://doi.org/10.1007/s00020-016-2326-x

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  • DOI: https://doi.org/10.1007/s00020-016-2326-x

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