Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Characterization of $(\sigma,\tau)-$ derivations on von Neumann
  algebras   Let $\mathcal A$ be a von Neumann algebra and $\mathcal M$ be a Banach
$\mathcal A-$module. It is shown that for every homomorphisms $\sigma, \tau$ on
$\mathcal A$, every bounded linear map $f:\mathcal A\to \mathcal M$ with
property that $f(p^2)=\sigma(p)f(p)+f(p)\tau(p)$ for every projection $p$ in
$\mathcal A$ is a $(\sigma,\tau)-$derivation. Also, it is shown that a bounded
linear map $f:\mathcal A \to \mathcal M $ which satisfies $f(ab)=
\sigma(a)f(b)+f(a)\tau(b)$ for all $a,b\in \mathcal A$ with $ab=S$, is a
$(\sigma,\tau)-$ derivation if $\tau(S)$ is left invertible for fixed $S$.

11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph