圆环上以有界调和函数为符号的Toeplitz算子的拟正规性

Quasi-Normality of Toeplitz Operators with Bounded Harmonic Functions on Rings

摘要: 函数空间算子理论一直是泛函分析研究中的一个重要分支之一。本文证明了在圆环Bergman空间上以有界调和函数u(z)=f(z)+g(z)，其中以f(z)=a_nzⁿ+a_mz^m，g(z)=b_nzⁿ+b_mz^m (其中m，n是非负整数)为符号的Toeplitz算子若是拟正规性，则一定是正规的.

Abstract: Functional space operator theory has always been an important branch of functional analysis. In this paper, we prove that there is the bounded harmonic function u(z)=f(z)+g(z) in the ring Bergman space, where Toeplitz operators with symbols of f(z)=a_nzⁿ+a_mz^m, g(z)=b_nzⁿ+b_mz^m (Where m and n are non-negative integers) must be normal if they are quasi-normal.