Admissibility and roughness of nonuniform exponential dichotomies for difference equations

In this paper we discuss on relationships between nonuniform exponential dichotomies of nonautonomous difference equations and admissibility for classes of weighted bounded solutions and show the roughness of nonuniform exponential dichotomies in the finite dimensional case. We give sufficient conditions for existence of nonuniform exponential dichotomies on Z0+ or Z0− separately, on Z0+ and Z0− simultaneously and on the whole ZZ. As an application, we use this result to discuss the roughness of nonuniform exponential dichotomies for difference equations on Z0+, Z0− and the whole ZZ separately and obtain better estimates for both the bound and the nonuniformity degree.