A remark on exponential dichotomies

A proof of the existence of an exponential dichotomy for the linear system x'(t) = A(t)x(t) is given, based on the admissibility of the pair (B(∞), B_A(∞)), where B(∞) is the space of continuous functions on the semiaxis J = [0,∞), values in Cⁿ and having a limit as t →∞, and B_A(∞) is the space of bounded functions f on J such that A ^-1 ∈ B(∞).