Discrete characterizations of h-dichotomy for linear discrete-time systems in Banach spaces

The present paper is focused of some concepts of dichotomy with growth rates (h-dichotomy, weak h-dichotomy) for linear discrete systems. These concepts use two types of dichotomy projections sequences (invariant and strongly invariant) and generalize some well-known dichotomy concepts. More precisely, necessary and sufficient conditions of Datko type are given using both invariant and strongly invariant projections sequences for h-dichotomy and weak h-dichotomy.