Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commutative subalgebras of the algebra of smooth operators   We consider the Fr\'echet ${}^*$-algebra $L(s',s)$ of the so-called smooth
operators, i.e. continuous linear operators from the dual $s'$ of the space $s$
of rapidly decreasing sequences into $s$. This algebra is a non-commutative
analogue of the algebra $s$. We characterize all closed commutative
${}^*$-subalgebras of $L(s',s)$ which are at the same time isomorphic to closed
${}^*$-subalgebras of $s$ and we provide an example of a closed commutative
${}^*$-subalgebra of $L(s',s)$ which cannot be embedded into $s$.

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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat