Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intersecting Jones projections   Let M be a von Neumann algebra on a Hilbert space H with a cyclic and
separating unit vector \Omega and let \omega be the faithful normal state on M
given by \omega(\cdot)=(\Omega,\cdot\Omega). Moreover, let {N_i :i\in I} be a
family of von Neumann subalgebras of M with faithful normal conditional
expectations E_i of M onto N_i satisfying \omega=\omega\circ E_i for all i\in I
and let N=\bigcap_{i\in I} N_i. We show that the projections e_i, e of H onto
the closed subspaces \bar{N_i\Omega} and \bar{N\Omega} respectively satisfy
e=\bigwedge_{i\in I}e_i.This proves a conjecture of V.F.R. Jones and F. Xu in
\cite{JonesXu04}.

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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph