Abstract

Given two unital C*-algebrasA, ℬ and their state spacesE A , Eℬ respectively, (A,E A ) is said to have (ℬ, Eℬ) as a hidden theory via a linear, positive, unit-preserving map L: ℬ →A if, for all ϕ εE A , L*ϕ can be decomposed in Eℬ into states with pointwise strictly less dispersion than that of ϕ. Conditions onA and L are found that exclude (A,E A ) from having a hidden theory via L. It is shown in particular that, ifA is simple, then no (ℬ, Eℬ) can be a hidden theory of (A,E A ) via a Jordan homomorphism; it is proved furthermore that, ifA is a UHF algebra, it cannot be embedded into a larger C*-algebra ℬ such that (ℬ, Eℬ) is a hidden theory of (A,E A ) via a conditional expectation from ℬ ontoA