Exponential dichotomy and (ℓp,ℓq)-admissibility on the half-line

We give necessary and sufficient conditions for uniform exponential dichotomy of discrete evolution families in terms of the admissibility of the pair . We prove that the admissibility of the pair is a sufficient condition for uniform exponential dichotomy of a discrete evolution family. This condition becomes necessary for discrete evolution families with uniform exponential growth if and only if p⩾q. As consequences, we obtain necessary and sufficient conditions for uniform exponential dichotomy of evolution families.