Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closability property of operator algebras generated by normal operators
  and operators of class $C_0$   An operator algebra $\mathcal{A}$ acting on a Hilbert space is said to have
the closability property if every densely defined linear transformation
commuting with $\mathcal{A}$ is closable. In this paper we study the
closability property of the von Neumann algebra consisting of the
multiplication operators on $L^2(\mu)$, and give necessary and sufficient
conditions for a normal operator $N$ such that the von Neumann algebra
generated by $N$ has the closability property. We also give necessary and
sufficient conditions for an operator $T$ of class $C_0$ such that the algebra
generated by $T$ in the weak operator topology and the algebra
$H^\infty(T)=\{u(T):u\in H^\infty\}$ have the closability property.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org