Necessary conditions and sufficient conditions for h-dichotomy of skew-evolution cocycles in Banach spaces

This study focuses on the problem of h-dichotomy for skew-evolution cocycles within Banach spaces. It outlines the necessary conditions and sufficient conditions for this framework, along with those for the notable concepts like exponential dichotomy, polynomial dichotomy and uniform h-dichotomy. These conditions are established through the use of strongly invariant families of projectors.