Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Additive mappings in algebras of unbounded operators preserving
  operators of rank one   Let $ \mathcal D$ be a dense linear manifold in a Hilbert space $\mathcal H$
and let $L^+(\mathcal D)$ be the *-algebra of all linear operators $A$ such
that $A \mathcal D \subset \mathcal D, A^* \mathcal D \subset \mathcal D$.
Denote by $F(\mathcal D)$ the *-ideal of $L^+(\mathcal D)$ consisting of all
finite-rank operators. A characterization of the structure of additive mappings
of $F(\mathcal D)$ preserving operators of rank one or projections of rank one
is given. The corresponding results for algebras of bounded operators on Banach
spaces were given by P. \u{S}emrl.

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The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
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The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics