Surjective isometries on the vector-valued differentiable function spaces

This paper investigates the surjective linear isometries between the differentiable function spaces C0n(Ω,E) and C0m(Σ,F) (where Ω,ΣΩ,Σ are open subsets of Euclidean spaces and E,FE,F are reflexive, strictly convex Banach spaces), and show that such isometries can be written as weighted composition operators.