Theorems of Perron type for uniform exponential dichotomy of linear skew-product semiflows

We study the connections between the uniform exponential dichotomy of a discrete linear skew-product semiflow and the uniform admissibility of the pair (c(0) (N, X), c(00) (N, X)). We give necessary and sufficient conditions for uniform exponential dichotomy of linear skew-product semiflows in terms of the uniform admissibility of the pairs (c(0) (N, X), c(00) (N, X)) and (C-0 (R+, X), C-00 (R+, X)), respectively. We generalize a dichotomy theorem due to Van Minh, Rabiger and Schnaubelt for the case of linear skew-product semiflows.