Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A II$_1$ factor approach to the Kadison-Singer problem   We show that the Kadison-Singer problem, asking whether the pure states of
the diagonal subalgebra $\ell^\infty\Bbb N\subset \Cal B(\ell^2\Bbb N)$ have
unique state extensions to $\Cal B(\ell^2\Bbb N)$, is equivalent to a similar
statement in II$_1$ factor framework, concerning the ultrapower inclusion
$D^\omega \subset R^\omega$, where $D$ is the Cartan subalgebra of the
hyperfinite II$_1$ factor $R$, and $\omega$ is a free ultraflter. While we do
not settle the problem in this latter form, we prove that if $A$ is any
singular maximal abelian subalgebra of $R$, then the inclusion $A^\omega
\subset R^\omega$ does satisfy the Kadison-Singer property.

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The categories of this paper are: econ
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
1
The categories of this paper are: cs