加权Bergman空间上的Toeplitz算子的数值域

The Numerical Range of a Toeplitz Operator on the Weighted Bergman Space

Bergman空间是一类特殊的Hilbert空间,其上可以定义Toeplitz算子,进而可以讨论此类算子的数值域.若将Bergman空间推广到加权Bergman空间,也可以讨论其上的Toeplitz算子的数值域.本文主要讨论加权Bergman空间上Toeplitz算子的数值域的性质,并得到了一些非常有意义的结论.

The Bergman space is a Hilbert space,we can define a Toeplitz operator on this space and study the numerical range of this operator.On the weighted Bergman space,we can also define a Toeplitz operator.In this paper,we discuss the properties of the numerical range of a Toeplitz operator on the weighted Bergman space,and get some useful results.