2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128554A 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.Operator AlgebrasFunctional Analysis46L10text