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Band-Dominated Operators on Bergman-Type Spaces

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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.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Shengkun Wu

  2. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Dechao Zheng

  3. Center of Mathematics, Chongqing University, Chongqing, 401331, China

    Dechao Zheng

Authors
  1. Shengkun Wu
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  2. Dechao Zheng
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Corresponding authors

Correspondence to Shengkun Wu or Dechao Zheng.

Additional information

The first author was supported by CSC (201906050022). This work was partially supported by NFSC (11531003).

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Wu, S., Zheng, D. Band-Dominated Operators on Bergman-Type Spaces. Acta Math Sci 43, 387–408 (2023). https://doi.org/10.1007/s10473-023-0122-7

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  • DOI: https://doi.org/10.1007/s10473-023-0122-7

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