Admissibility versus nonuniform exponential behavior for noninvertible cocycles
From the abstract: We study the relation between the notions of exponential dichotomy and admissibility for a nonautonomous dynamics with discrete time. More precisely, we consider \(\mathbb{Z}\)-cocycles defined by a sequence of linear operators in a Banach space, and we give criteria for the existence of an exponential dichotomy in terms of the admissibility of the pairs \((\ell^p,\ell^q)\) of spaces of sequences, with \(p\leq q\) and \((p,q)\neq(1,\infty)\). We extend the existing results in several directions. Namely, we consider the general case of nonuniform exponential dichotomies; we consider \(\mathbb{Z}\)-cocycles and not only \(\mathbb{N}\)-cocycles; and we consider exponential dichotomies that need not be invertible in the stable direction. We also exhibit a collection of admissible pairs of spaces of sequences for any nonuniform exponential dichotomy.
scientific article; zbMATH DE number 6157253