Exponential dichotomy and ( p, q)-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 (lp(N,X), l q 0 (N,X)). We prove that the admissibility of the pair (lp(N,X), l q 0 (N,X)) 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.  2005 Elsevier Inc. All rights reserved