# Classically Normal Pure States

Classically Normal Pure States A pure state f of a von Neumann algebra $$\mathcal M$$ is called classically normal if f is normal on any von Neumann subalgebra of $$\mathcal M$$ 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 ∈M such that pMp is a factor of type I ∞, II, or III. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Classically Normal Pure States

, Volume 11 (4) – Sep 26, 2007
9 pages
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Publisher
Birkhäuser-Verlag
Copyright
Copyright © 2007 by Birkhäuser Verlag, Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-007-2123-5
Publisher site
See Article on Publisher Site

### Abstract

A pure state f of a von Neumann algebra $$\mathcal M$$ is called classically normal if f is normal on any von Neumann subalgebra of $$\mathcal M$$ 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 ∈M such that pMp is a factor of type I ∞, II, or III.

### Journal

PositivitySpringer Journals

Published: Sep 26, 2007

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