Hyperbolic composition operators on Orlicz spaces

TL;DR

This paper investigates the shadowing property of composition operators on Orlicz spaces, establishing conditions under which these operators exhibit hyperbolic behavior and extending known results from L^p-spaces.

Contribution

It provides new equivalent conditions for shadowing and shows the equivalence of hyperbolicity and shadowing for composition operators on Orlicz spaces.

Findings

Shadowing property characterized by equivalent conditions

Hyperbolicity and shadowing are equivalent for these operators

Results extend known properties from L^p-spaces

Abstract

In the present paper we provide some equivalent conditions for composition operators to have shadowing property on Orlicz space. Also, we obtain that for the composition operators on Orlicz spaces the notions of generalized hyperbolicity and the shadowing property coincide. The results of this paper extends similar results on L^p-spaces.