Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abundance of invariant and almost invariant pure states of C*-dynamical
  systems   We show that invariant states of C*-dynamical systems can be approximated in
the weak*-topology by invariant pure states, or almost invariant pure states,
under various circumstances.

15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc