Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of a family of non almost periodic free Araki-Woods
  factors   We obtain a complete classification of a large class of non almost periodic
free Araki-Woods factors $\Gamma(\mu,m)"$ up to isomorphism. We do this by
showing that free Araki-Woods factors $\Gamma(\mu, m)"$ arising from finite
symmetric Borel measures $\mu$ on $\mathbf{R}$ whose atomic part $\mu_a$ is
nonzero and not concentrated on $\{0\}$ have the joint measure class $\mathcal
C(\bigvee_{k \geq 1} \mu^{\ast k})$ as an invariant. Our key technical result
is a deformation/rigidity criterion for the unitary conjugacy of two faithful
normal states. We use this to also deduce rigidity and classification theorems
for free product von Neumann algebras.

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The categories of this paper are: hep-ex
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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: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg