Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positivity of $2\times 2$ block matrices of operators   We review some of the significant generalizations and applications of the
celebrated Douglas theorem on the equivalence of factorization, range
inclusion, and majorization of operators. We then apply it to find a
characterization of the positivity of $2\times 2$ block matrices of operators
in Hilbert spaces and finally describe the nature of such block matrices and
provide several ways for showing their positivity.

9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph