Radial Operators on the Weighted Bergman Spaces over the Polydisk

作     者：Ran LI Yu Feng LU 

作者机构：School of Mathematical Sciences Dalian University of Technology 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2019年第35卷第2期

页      面：227-238页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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

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

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.