Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isometric stability property of certain Banach spaces   Let $E$ be one of the spaces $C(K)$ and $L_1$, $F$ be an arbitrary Banach
space, $p>1,$ and $(X,\sigma)$ be a space with a finite measure. We prove that
$E$ is isometric to a subspace of the Lebesgue-Bochner space $L_p(X;F)$ only if
$E$ is isometric to a subspace of $F.$ Moreover, every isometry $T$ from $E$
into $L_p(X;F)$ has the form $Te(x)=h(x)U(x)e, e\in E,$ where $h:X\rightarrow
R$ is a measurable function and, for every $x\in X,$ $U(x)$ is an isometry from
$E$ to $F.$

5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org