Admissibility for nonuniform exponential contractions

We study the relation between the notions of nonuniform exponential stability and admissibility. In particular, using appropriate adapted norms (which can be seen as Lyapunov norms), we show that if any of their associated Lp spaces, with p∈(1,∞], is admissible for a given evolution process, then this process is a nonuniform exponential contraction. We also provide a collection of admissible Banach spaces for any given nonuniform exponential contraction.