Radial Operators on the Weighted Bergman Spaces over the Polydisk  

作　　者：Ran LI Yu Feng LU 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology

出　　处：《Acta Mathematica Sinica,English Series》2019年第2期227-238,共12页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11671065)

摘　　要：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.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.

关 键 词：RADIAL OPERATORS (m λ)-Berezin transform weighted BERGMAN SPACES TOEPLITZ OPERATORS 

分 类 号：O1[理学—数学]