Delay Equations and Admissible Spaces

We establish the equivalence of admissibility and hyperbolicity for a nonautonomous delay equation. We consider a large class of admissible pairs of Banach spaces defined in terms of admissible spaces satisfying certain general properties. This required various nontrivial modifications of the existing theory, such as a delicate choice of perturbations to obtain the stable and unstable spaces of an exponential dichotomy.