Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Into isometries of $C_0(X,E)$'s   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).

0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga