BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES*

doi:10.1007/s10473-023-0122-7

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 387-408.doi: 10.1007/s10473-023-0122-7

BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES^*

Shengkun Wu¹, Dechao Zhen²

1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;
2. Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA Center of Mathematics, Chongqing University, Chongqing 401331, China

收稿日期:2021-04-15 修回日期:2022-06-12 发布日期:2023-03-01
基金资助:
*CSC (201906050022). This work was partially supported by NFSC (11531003).

BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES^*

Shengkun Wu¹, Dechao Zhen²

1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;
2. Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA Center of Mathematics, Chongqing University, Chongqing 401331, China

Received:2021-04-15 Revised:2022-06-12 Published:2023-03-01
About author:Shengkun Wu,E-mail: shengkunwu@foxmail.com;Dechao Zhen,E-mail: dechao.zheng@vanderbilt.edu
Supported by:
*CSC (201906050022). This work was partially supported by NFSC (11531003).

摘要/Abstract

摘要： In this paper, we study band-dominated operators on Bergman-type spaces and prove that the $C^*$-algebra of band-dominated operators is equal to the essential commutant of Toeplitz operators with a symbol in the set of bounded vanishing Lipschitz functions. On the Bergman space and the Fock space, we show that the $C^*$-algebra of band-dominated operators equals the Toeplitz algebra.

关键词: Band-dominated operators, Bergman-type space, Essential commutant

Abstract: In this paper, we study band-dominated operators on Bergman-type spaces and prove that the $C^*$-algebra of band-dominated operators is equal to the essential commutant of Toeplitz operators with a symbol in the set of bounded vanishing Lipschitz functions. On the Bergman space and the Fock space, we show that the $C^*$-algebra of band-dominated operators equals the Toeplitz algebra.

Key words: Band-dominated operators, Bergman-type space, Essential commutant

Shengkun Wu, Dechao Zhen. BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES^*[J]. 数学物理学报(英文版), 2023, 43(1): 387-408.

Shengkun Wu, Dechao Zhen. BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES^*[J]. Acta mathematica scientia,Series B, 2023, 43(1): 387-408.

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BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES^*

BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES^*

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