模型空间上截断Toeplitz算子的范数和本质范数

Norm and essential norm of truncated Toeplitz operators on model spaces

借助分布函数不等式,本文得到模型空间上截断Toeplitz算子的范数和本质范数的一个上界和下界.作为应用,本文给出有界符号的截断Toeplitz紧性的一个充分必要条件.

In this paper,we obtain an upper bound and a lower bound of the norm and essential norm of truncated Toeplitz operators on model spaces by the distribution function inequality.As a consequence,we get a necessary and sufficient condition of compactness of truncated Toeplitz operators on model spaces.