International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 3895-3908
doi:10.1155/IJMMS.2005.3895
Nonwandering operators in Banach space
Lixin Tian
, Jiangbo Zhou
, Xun Liu
and Guangsheng Zhong
Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Jiangsu, Zhenjiang 212013, China
Abstract
We introduce nonwandering operators in infinite-dimensional separable Banach space. They are new linear chaotic operators and are relative to hypercylic operators, but different from them. Firstly, we show some examples for nonwandering operators in some typical infinite-dimensional Banach spaces, including Banach sequence space and physical background space. Then we present some properties of nonwandering operators and the spectra decomposition of invertible nonwandering operators. Finally, we obtain that invertible nonwandering operators are locally structurally stable.