Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizations of operator order for k strictly positive operators   Let $A_{i}\ (i=1, 2, ..., k)$ be bounded linear operators on a Hilbert space.
This paper aims to show characterizations of operator order $A_{k}\geq
A_{k-1}\geq...\geq A_{2}\geq A_{1}>0$ in terms of operator inequalities.
Afterwards, an application of the characterizations is given to operator
equalities due to Douglas's majorization and factorization theorem.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an