Surjective isometries between function spaces

Let X be a compact Hausdorff space. We denote by C(X) the Banach space of all continuous complex valued functions on X with respect to the supremum norm. A function space A on X is a normed linear subspace of C(X) that contains the constant function 1 and separates the points of X. We give a necessary and sufficient condition for a surjective distance preserving map between two function spaces be represented by a weighted composition operator.