Stability of Discrete Dichotomies for Linear Difference Systems

Abstract

In this paper we show that the discrete (h,k)-dichotomies are stabel under summable perturbations and they can be characterized in terms of the admissibility of pairs of sequential spaces. As an application we obtain that a linear diagonal system with Levinson dichotomy can by viewed as a system displaying a collection of h-dichotomies which are stable under summable perturbations.