Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditions Implying Commutativity of Unbounded Self-adjoint Operators
  and Related Topics   Let $B$ be a bounded self-adjoint operator and let $A$ be a nonnegative
self-adjoint unbounded operator. It is shown that if $BA$ is normal, it must be
self-adjoint and so must be $AB$. Commutativity is necessary and sufficient for
this result. If $AB$ is normal, it must be self-adjoint and $BA$ is essentially
self-adjoint. Although the two problems seem to be alike, two different and
quite interesting approaches are used to tackle each one of them.

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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
18
The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn