Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (1): 387-408.doi: 10.1007/s10473-023-0122-7

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Shengkun Wu1, Dechao Zhen2   

  1. 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:;Dechao Zhen,E-mail:
  • Supported by:
    *CSC (201906050022). This work was partially supported by NFSC (11531003).

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