Hypercyclic与Supercyclic的Toeplitz算子

Hypercyclic and Supercyclic Toeplitz Operator

首先运用函数论的方法,阐述了在Hardy空间以及Bergman空间上,当符号φ满足某种条件时,余解析Toeplitz算子Tφ为Hypercyclic或Supercyclic算子.其次运用谱的知识及指标理论,阐述了当符号φ满足某种条件时,Toeplitz算子Tφ位于Hc(H)或Sc(H)中.

It is proved that there are some Hypercyclic and Supercyclic operators in the class of co-analytic Toeplitz operators in Hardy space and Bergman space. Applying spectrum and index theorys, we also prove that Toeplitz operator T_φ belongs to H_c(H) or S_c(H) when the symbol φ satisfies certain conditions.