English

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}
}
R2 v1 2026-06-21T08:25:50.314Z