International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 3895-3908
Nonwandering operators in Banach space
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.