Admissibility for exponential dichotomies in average

We characterize completely the notion of an exponential dichotomy in average in terms of an admissibility property. The notion corresponds to a generalization of that of an exponential dichotomy to measurable cocycles acting on L-1 functions with respect to a given probability measure. The admissibility property is described in terms of the injectivity and surjectivity of a certain linear operator in the space of bounded sequences of L-1 functions. The characterization is then used to establish in a simple manner the robustness of the notion, in the sense that it persists under sufficiently small linear perturbations. We note that we consider both Z-cocycles and N-cocycles.