Radial Operators on the Weighted Bergman Spaces over the Polydisk
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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.
KeywordsRadial operators (m, λ)-Berezin transform weighted Bergman spaces Toeplitz operators
MR(2010) Subject Classification47B35 47B37 47A58
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We thank the referees for their time and comments.
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