Abstract
In this paper, we study radial operators in Toeplitz algebra on the weighted Bergman spaces over the polydisk by the (m, λ)-Berezin transform and find that a radial operator can be approximated in norm by Toeplitz operators without any conditions. We prove that the compactness of a radial operator is equivalent to the property of vanishing of its (0, λ)-Berezin transform on the boundary. In addition, we show that an operator S is radial if and only if its (m, λ)-Berezin transform is a separately radial function.
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We thank the referees for their time and comments.
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Supported by the National Natural Science Foundation of China (Grant No. 11671065)
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Li, R., Lu, Y.F. Radial Operators on the Weighted Bergman Spaces over the Polydisk. Acta. Math. Sin.-English Ser. 35, 227–238 (2019). https://doi.org/10.1007/s10114-018-8132-4
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DOI: https://doi.org/10.1007/s10114-018-8132-4