International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 3895-3908

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

Received 8 November 2004; Revised 27 October 2005

Copyright © 2005 Lixin Tian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.