Into isometries of $C_0(X,E)$'s

Details Into isometries of $C_0(X,E)$'s Into isometries of $C_0(X,E)$'s

1996-07-30

arxiv.org/abs/math/9607211v1

Mathematics

Functional Analysis

Scientific paper

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).

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