  In a Banach space, assuming that a linear nonautonomous differential equation
$v'=A(t)v$ admits a very general type of trichotomy, we establish conditions
for the existence of global Lipschitz invariant center manifold of the
perturbed equation $v'=A(t)v+f(t,v)$. Our results not only improve results
already existing in the literature, as well include new cases.
