Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A closed densely defined operator $T$ such that both $T$ and $T^*$ are
  injective and paranormal yet $T$ is not normal   In this note, we give an example of a densely defined closed one-to-one
paranormal operator $T$ whose adjoint is also injective and paranormal, but $T$
fails to be normal.

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
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th