On the robustness of nonuniform exponential trichotomies

For linear equations in a Banach space, we show that the existence of a nonuniform exponential trichotomy for x′=A(t)xx′=A(t)x persists under sufficiently small C1C1 perturbations B(t,λ)xB(t,λ)x, in such a way that the stable, unstable and center subspaces are of class C1C1 in λ.