Banach-stone theorem for banach lattice valued continuous functions

Let X and Y be compact Hausdorff spaces, E be a Banach lattice and F be an AM space with unit. Let π: C(X,E) → C(Y,F) be a Riesz isomorphism such that 0 ∉ f(X) if and only if 0 ∉ π(f)(Y) for each f ∈ C(X, E). We prove that X is homeomorphic to Y and E is Riesz isomorphic to F. This generalizes some known results.