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For a 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 in pairs of spaces (ℓ p , ℓ q ), with p and q not necessarily equal. This includes the notion of a nonuniform exponential dichotomy as a very special case. Moreover, we consider a general noninvertible dynamics and a strong nonuniform exponential behavior. The latter is the typical situation from the point of view of smooth ergodic theory.

Nonuniform Hyperbolicity and Admissibility