加权Bergman空间上具有调和符号的斜Toeplitz算子的正规性及亚正规性

The Normality and Hyponormality of Slant Toeplitz Operators with Harmonic Symbols on the Weighted Bergman Spaces

本文对单位圆盘的加权Bergman空间上斜Toeplitz算子的正规性及亚正规性展开研究,得到了以有界解析函数、共轭解析函数及调和多项式函数为符号的斜Toeplitz算子是正规算子或亚正规算子的充要条件是其符号函数是零函数,当且仅当该类算子是零算子,也得到了该类算子的正规性和亚正规性是等价的。

The normality and hyponormality of slant Toeplitz operators on the weighted Bergman space of the unit disk are studied, and obtain the sufficient and necessary conditions for slant Toeplitz operators with bounded analytic function, conjugate analytic function and harmonic polynomial function to be normal or hyponormal are that their symbol functions are zero function, if and only if such opera-tors are zero operator, and also get the normality and the hyponormality of such operators are equivalent.