Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Radon-Nikodym theorem for von Neumann algebras   In this paper we present a generalization of the Radon-Nikodym theorem proved
by Pedersen and Takesaki. Given a normal, semifinite and faithful (n.s.f.)
weight $\phi$ on a von Neumann algebra M and a strictly positive operator
$\delta$, affiliated with M and satisfying a certain relative invariance
property with respect to the modular automorphism group $\sigma^\phi$ of
$\phi$, with a strictly positive operator as the invariance factor, we
construct the n.s.f. weight $\phi(\delta^{1/2} . \delta^{1/2})$. All the n.s.f.
weights on M whose modular automorphisms commute with $\sigma^\phi$ are of this
form, the invariance factor being affiliated with the centre of M. All the
n.s.f. weights which are relatively invariant under $\sigma^\phi$ are of this
form, the invariance factor being a scalar.

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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org