Acta Mathematica Sinica, English Series

, Volume 35, Issue 2, pp 227–238

# Radial Operators on the Weighted Bergman Spaces over the Polydisk

• Ran Li
• Yu Feng Lu
Article

## 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.

## Keywords

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

## MR(2010) Subject Classification

47B35 47B37 47A58

## Notes

### Acknowledgements

We thank the referees for their time and comments.

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