On the asymptotic behavior of perturbed strongly continuous semigroups

For a strongly continuous semigroup (T(t))(t greater than or equal to0) wit h generator. A on a Banach space X and an A - bounded perturbation B we cha racterize norm continuity and compactness of the terms in the Dyson-Phillip s series of the perturbed semigroup (S(t))(t >0). This allows us to charact erize uniform exponential stability of(S(t))(t >0) by spectral conditions o n (T(t))(t >0) and A + B. The results are applied to a delay differential e quation.