Abstract
For a general one-sided nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of an exponential dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility of bounded solutions. As a nontrivial application, we establish the robustness of the notion under sufficiently small parameterized perturbations. Moreover, we show that if the perturbations are Lipschitz or of class C^1 on the parameter, then the same happens to the projections onto the stable spaces of the perturbation.
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