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m-Berezin Transform on the Polydisk

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Abstract.

m-Berezin transforms are introduced for bounded operators on the Bergman space of the polydisk. We show several properties of m-Berezin transform and use them to show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary of the polydisk. A useful and sharp approximate identity of its m-Berezin transforms is obtained for a bounded operator.

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Authors and Affiliations

  1. Department of Mathematics, Hanshin University, Gyeonggi, 447-791, Korea

    Kyesook Nam

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

    Dechao Zheng

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  1. Kyesook Nam
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  2. Dechao Zheng
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Correspondence to Kyesook Nam.

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Nam, K., Zheng, D. m-Berezin Transform on the Polydisk. Integr. equ. oper. theory 56, 93–113 (2006). https://doi.org/10.1007/s00020-005-1409-x

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  • DOI: https://doi.org/10.1007/s00020-005-1409-x

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