On the eventual shadowing property for linear operators

Aponte J.; Carraso-Olivera D.; Villavienio H. · Bulletin of Computational Applied Mathematics (2024)

Resumen

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.

Instituciones: Universidad Nacional de Ingeniería