Hardy空间上的斜Toeplitz算子的极小约化子空间

Minimal Reducing Subspaces of Slant Toeplitz Operators on Hardy Space

首先介绍了一些相关的基础知识并引入斜Toeplitz算子与Hardy空间的概念,然后将Hardy空间分解为3个互不相交的子空间;研究单位圆周Hardy空间上以z N为符号的斜Toeplitz算子的约化子空间。证明得到这3部分都是斜Toeplitz算子的约化子空间;最后给出极小约化子空间的具体形式及其个数与N的关系。

We first introduce some basic knowledge and the concepts of slant Toeplitz operator and Hardy space and then decompose Hardy space into three disjoint subspaces.We study the reducing subspaces of the slant Toeplitz operator with the symbol z N in the Hardy space of the unit circle.It is proved that these three parts are reducing subspaces of the slant Toeplitz operator.Finally we give the concrete form of minimal reducing subspaces and obtain the relationship between the number of the minimal reducing subspaces and N.