abstract 100

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

100

On the eventual shadowing property for linear operators (Research Paper)

Jesús Aponte, Dante Carrasco-Olivera, Helmuth Villavicencio.

In this paper, we prove that a bounded linear operator of a Banach space has an eventually shadowable point if and only if it has the eventual shadowing property. Secondly,  we characterize eventual shadowableness of bounded linear operators using bounded sequences. Next, we prove that in the finite-dimensional case the eventual shadowing property coincides with the classical shadowing property. Finally, we prove that if a bounded linear operator is positively expansive and has the eventual shadowing property, the origin is the only non-wandering point.

Keywords: Linear operator; Banach space; shadowable point; eventually shadowable point; expansivity; equicontinuous.

Cite this paper:

Aponte J., Carrasco-Olivera D. , Villavicencio H.

On the eventual shadowing property for linear operators.

Bull. Comput. Appl. Math. (Bull CompAMa),

Vol. 12, No.2 pp.xx-xx, 2024.