Toeplitz算子的双正规性和M-亚正规性

Binormality and M-hyponormality of the Toeplitz operators

主要研究(加权)Bergman空间和Fock空间上Toeplitz算子的双正规性和M-亚正规性:①给出了Bergman空间上以拟齐次函数e i kθf(r)为符号的Toeplitz算子的拟正规性的充分必要条件,进而研究了以e i kθf(r)为符号的Toeplitz算子的双正规性;给出了Bergman空间上以解析多项式∑n[]i=0 a iz i为符号的Toeplitz算子的双正规性的充分必要条件及其与Bergman内函数的关系;②分别在加权Bergman空间和Fock空间上研究了以az+b-z-为符号的Toeplitz算子的M-亚正规性,进一步给出了亚正规性和M-亚正规性的等价关系.

In this paper,we mainly study the binormality and M-hyponormality of Toeplitz operators in(weighted)Bergman spaces and Fock space:①The necessary and sufficient conditions of quasi-normality of Toeplitz operator with quasi-homogeneous function e i kθf(r)in Bergman space are given,and then the binormality of Toeplitz operator with e i kθf(r)is studied.The necessary and sufficient conditions for the binormality of Toeplitz operator with analytic polynomial∑n[]i=0 a iz i in Bergman space and its relationship with Bergman inner function are given.②M-hyponormality of Toeplitz operator with az+b-z-is studied in weighted Bergman space and Fock space respectively,and the equivalence relation between subnormality and M-hyponormality is further given.