Toeplitz算子■的双稳定性

Double stability of Toeplitz operator ■

由Hilbert空间分次模理论可知,对某个算子双稳定性的刻画可以对该算子不可约性的证明起到关键性作用。本文从Toeplitz算子T z+w的结构出发,利用分次模理论,得到了在一般函数空间中由Toeplitz算子T z+w所诱导的分次模具有双稳定性的结果。

It can be known from the graded module theory in Hilbert space that the characterization of double stability of an operator can play a key role in proving the irreducibility of the operator.In this paper,beginning with the structure of Toeplitz operator T z+w and using the theory of graded module,we obtain the fact that the graded module induced by Toeplitz operator T z+w has double stability in general function space.