Universal fundamental systems in ordered Banach spaces

Abstract.

Let E be a separable Banach space ordered by a reproducing cone with empty interior. We prove the existence of operator functions A : [0, ∞) → P (P the cone of monotone increasing linear operators) and of initial values x₀ such that the solution of x ′(t) = A(t) x(t), x(0) = x₀, is dense in E.