Acta Mathematica Sinica, English Series

, Volume 35, Issue 2, pp 227–238 | Cite as

Radial Operators on the Weighted Bergman Spaces over the Polydisk

  • Ran LiEmail author
  • Yu Feng Lu


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.


Radial operators (m, λ)-Berezin transform weighted Bergman spaces Toeplitz operators 

MR(2010) Subject Classification

47B35 47B37 47A58 


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We thank the referees for their time and comments.


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianP. R. China

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