Robustness of nonuniform exponential trichotomies in Banach spaces

We establish the robustness under sufficiently small linear perturbations of nonuniform exponential trichotomies defined by linear equations x^′=A(t)x in Banach spaces. We also establish the continuous dependence on the perturbation of the constants in the notion of trichotomy. We consider both trichotomies in semi-infinite intervals and trichotomies in R.