Surjective isometries on vector-valued differentiable function spaces

Abstract

In this article, we investigate the surjective linear isometries between the differentiable function spaces $C_0^p(X,E)$ and $C_0^q(Y,F)$, where $X$, $Y$ are open subsets of $\mathbb{R}$ and $E$, $F$ are strictly convex Banach spaces with dimension greater than $1$. We show that such isometries can be written as weighted composition operators.