Classically normal pure states

Details Classically normal pure states Classically normal pure states

2007-05-07

arxiv.org/abs/0705.0992v1

Mathematics

Operator Algebras

Scientific paper

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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