非游荡算子与超循环算子

Nonwandering Operators and Supercyclic Operators

本文研究无穷维空间中一类具有混沌特性的算子:非游荡算子。主要结论是希尔伯特空间中移位算子及与它交换的算子,在常数意义下都是非游荡算子。并在非游荡集为紧集时,给出非游荡算子的超循环分解。

Studied are the nonwandering operators of chaotic properties in infinite dimensional linear space. The main results are given as follows: the shift operators in Hilbert space and operators exchanging for them are nonwandering operators in the sense of a constant. When nonwandering set of the nonwarder-ing operator is compact, a result is given concerning the relationship between no nwandering operators and supercyclic operators.