Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple examples of non closable paranormal operators   In this note, we give an example of a densely defined non-closable paranormal
operator. Then, we give another example of a densely defined closable
paranormal operator whose closure fails to be paranormal. These two examples
are simpler than those which first appeared in [1]. It is worth noticing that
our first example tells us that the adjoint of a densely defined paranormal
operator may have a trivial domain.

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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci