Jauch-Piron states on von Neumann algebras (Q1323414)

We give a detailed analysis of Jauch-Piron states on a von Neumann algebra \(M\). When \(M\) is \(\sigma\)-finite it is shown that all Jauch-Piron states are non-singular if \(M\) is properly infinite and are regular if \(M\) is Type III whereas, if \(M\) is finite, singular Jauch-Piron states often exist. Non-\(\sigma\)-finite algebras \(M\) are also discussed and it is shown that Jauch-Piron pure states are \(\sigma\)-additive whenever \(M\) has no abelian part.