Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizations of centralizable mappings on algebras of locally
  measurable operators   A linear mapping $\phi$ from an algebra $\mathcal{A}$ into its bimodule
$\mathcal M$ is called a centralizable mapping at $G\in\mathcal{A}$ if
$\phi(AB)=\phi(A)B=A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$.
In this paper, we prove that if $\mathcal M$ is a von Neumann algebra without
direct summands of type $\mathrm{I}_1$ and type $\mathrm{II}$, $\mathcal A$ is
a $*$-subalgebra with $\mathcal M\subseteq\mathcal A\subseteq LS(\mathcal{M})$
and $G$ is a fixed element in $\mathcal A$, then every continuous (with respect
to the local measure topology $t(\mathcal M)$) centralizable mapping at $G$
from $\mathcal A$ into $\mathcal M$ is a centralizer.

34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex