Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subideals of operators   A subideal is an ideal of an ideal of B(H) and a principal subideal is a
principal ideal of an ideal of B(H). We determine necessary and sufficient
conditions for a principal subideal to be an ideal of B(H). This generalizes to
arbitrary ideals the 1983 work of Fong and Radjavi characterizing principal
subideals of the ideal of compact operators that are also ideals of B(H). We
then characterize all principal subideals. We also investigate the lattice
structure of subideals as part of the general study of ideal lattices such as
the often studied lattice structure of ideals of B(H). This study of subideals
and the study of elementary operators with coefficient constraints are closely
related.

7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph