The relation between the notions of nonuniform asymptotic stability and admissibility is considered. Using appropriate Lyapunov norms, it is showed that if any of their associated spaces, with , is admissible for a given evolution process, then this process is a nonuniform contraction and dichotomy. A collection of admissible Banach spaces for any given nonuniform contraction and dichotomy is provided.
"Admissibility for Nonuniform Contraction and Dichotomy." Abstr. Appl. Anal. 2012 (SI07) 1 - 23, 2012. https://doi.org/10.1155/2012/741696