Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lomonosov's theorem cannot be extended to chains of four operators   We show that the celebrated Lomonosov theorem cannot be improved by
increasing the number of commuting operators. Specifically, we prove that if T
is the operator on l_1 without a non-trivial closed invariant subspace
constructed by C.J.Read, then there are three operators S_1, S_2 and K
(non-multiples of the identity) such that T commutes with S_1, S_1 commutes
with S_2, S_2 commutes with K, and K is compact. It is also shown that the
commutant of T contains only series of T.

11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int