Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncompactness and noncompleteness in isometries of Lipschitz spaces   We solve the following three questions concerning surjective linear
isometries between spaces of Lipschitz functions $\mathrm{Lip}(X,E)$ and
$\mathrm{Lip}(Y,F)$, for strictly convex normed spaces $E$ and $F$ and metric
spaces $X$ and $Y$: \begin{enumerate} \item Characterize those base spaces $X$
and $Y$ for which all isometries are weighted composition maps. \item Give a
condition independent of base spaces under which all isometries are weighted
composition maps. \item Provide the general form of an isometry, both when it
is a weighted composition map and when it is not. \end{enumerate} In
particular, we prove that requirements of completeness on $X$ and $Y$ are not
necessary when $E$ and $F$ are not complete, which is in sharp contrast with
results known in the scalar context.

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The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org