Classically normal pure states
Operator Algebras
2007-05-23 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.0705.0992,
title = {Classically normal pure states},
author = {Charles Akemann and Nik Weaver},
journal= {arXiv preprint arXiv:0705.0992},
year = {2007}
}