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arXiv · 0705.0992

Classically normal pure states

Charles Akemann·Nik Weaver
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Abstract

A pure state f of a von Neumann algebra M is called classically normal if f is normal on any von Neumann subalgebra of M on which f is multiplicative. Assuming the continuum hypothesis, a separably represented von Neumann algebra M has classically normal, singular pure states iff there is a central projection p in M such that Mp is a factor of type I_\infty, II, or III.

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Charles Akemann, Nik Weaver. 2007-05-07. Classically normal pure states. https://arxiv.org/abs/0705.0992

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