Abstract
We give characterizations of the hyperbolicity of a nonautonomous one-sided dynamics defined by a sequence of linear operators, in terms of the hyperbolicity of an associated evolution map defined on a Banach space of sequences. We consider a large family of spaces of sequences besides $$L^p$$ spaces. Moreover, we discuss the general cases when the dynamics may be invertible only along the unstable direction and of a general nonuniform exponential behavior of the dynamics given by a sequence of norms instead of a single norm.
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