  Suppose $X$ and $Y$ are locally compact Hausdorff spaces, $E$ and $F$ are
Banach spaces and $F$ is strictly convex. We show that every linear isometry
$T$ from $C_0(X,E)$ {\em into} $C_0(Y,F)$ is essentially a weighted composition
operator $Tf(y) = h(y) (f(\varphi(y)))$. This supplements results of Jerison
(when $T$ is onto) and Cambern (when $X,Y$ are compact).
