Admissibility and uniform dichotomy for evolution families

摘要

The present paper studies the problem of uniform dichotomy for evolution families in general. We obtain a result identical with the one for differential systems in infinite dimensional spaces (Massera and Schaffer in Linear Diferential Equations and Function Spaces, Academic Press, New York, 1966, Preda in An Univ Timisoara Ser Stiint Mat 17:65-71, 1979), as well as the existence of a family of projectors compatible with the evolution family. This family of projectors has similar properties as the one obtained by van Minh et al. (Integr Equ Oper Theory 32:332-353, 1998) and by van Minh and Thieu Huy (J Math Anal Appl 261:28-44, 2001), but for evolution families with uniform exponential growth.