Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nest algebras in $c_1$   In this paper we address some basic questions of the Banach space structure
of the nest algebras in the trace class; in particular, we study whether any
two of them are isomorphic to each other, and show that the nest algebras in
the trace class have bases. We construct three non-isomorphic examples of nest
algebras in $c_1$; present a new proof of the primarity of $c_1$ (Arazy, [Ar1],
[Ar2]), and prove that $K(H)$, and the nest algebras in $B(H)$ are primary.

37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org