Hamhalter, Jan States on \(W^*\)-algebras and orthogonal vector measures. (English) Zbl 0743.46063 Proc. Am. Math. Soc. 110, No. 3, 803-806 (1990). Summary: We show that every state on a \(W^*\)-algebra \({\mathcal A}\) without type \(I_ 2\) direct summand is induced by an orthogonal vector measure on \({\mathcal A}\). This result may find an application in quantum stochastics. Particularly, it allows us to find a simple formula for the transition probability between two states on \({\mathcal A}\). Cited in 2 ReviewsCited in 4 Documents MSC: 46L30 States of selfadjoint operator algebras 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 46L10 General theory of von Neumann algebras Keywords:state on a \(W^*\)-algebra; orthogonal vector measure; transition probability between two states PDFBibTeX XMLCite \textit{J. Hamhalter}, Proc. Am. Math. Soc. 110, No. 3, 803--806 (1990; Zbl 0743.46063) Full Text: DOI