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

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• 作者：Xing-Tang Dong ; Kehe Zhu
• 关键词：Toeplitz operator ; Bergman space ; pluriharmonic Bergman space ; commutator ; semi ; commutator ; monomial symbol
• 刊名：Integral Equations and Operator Theory
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：86
• 期：2
• 页码：271-300
• 全文大小：714 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8989
• 卷排序：86

文摘

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.