Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weakly closed Lie modules of nest algebras   Let $\mathcal{T}(\mathcal{N})$ be a nest algebra of operators on Hilbert
space and let $\mathcal{L}$ be a weakly closed Lie
$\mathcal{T}(\mathcal{N})$-module. We construct explicitly the largest possible
weakly closed $\mathcal{T}(\mathcal{N})$-bimodule $\mathcal{J}(\mathcal{L})$
and a weakly closed $\mathcal{T}(\mathcal{N})$-bimodule
$\mathcal{K}(\mathcal{L})$ such that \[ \mathcal{J}(\mathcal{L})\subseteq
\mathcal{L} \subseteq \mathcal{K}(\mathcal{L})
+\mathcal{D}_{\mathcal{K}(\mathcal{L})}, \]
  $[\mathcal{K}(\mathcal{L}), \mathcal{T}(\mathcal{N})]\subseteq \mathcal{L}$
and $\mathcal{D}_{\mathcal{K}(\mathcal{L})}$ is a von Neumann subalgebra of the
diagonal $\mathcal{T}(\mathcal{N})\cap \mathcal{T}(\mathcal{N})^*$.

9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph