Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Range-kernel characterizations of operators which are adjoint of each
  other   We provide necessary and sufficient conditions for a pair $S,T$ of Hilbert
space operators in order that they satisfy $S^*=T$ and $T^*=S$. As a main
result we establish an improvement of von Neumann's classical theorem on the
positive self-adjointness of $S^*S$ for two variables. We also give some new
characterizations of self-adjointness and skew-adjointness of operators, not
requiring their symmetry or skew-symmetry, respectively.

7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin