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We analyze the existence of (no past) exponential dichotomies for a well-posed autonomous differential equation (that generates aC0-semigroup ). The novelty of our approach consists in the fact that we do not assume theT(t)-invariance of the unstable manifolds. Roughly speaking, we prove that if the solution of the corresponding inhomogeneous difference equation belongs to any sequence space (on which the right shift is an isometry) for every inhomogeneity from the same class of sequencedoi:10.1155/2012/527647 fatcat:7gqtz772hrbmhof2whc5oqbs5q