States on 𝑊*-algebras and orthogonal vector measures

Hamhalter, Jan

doi:10.1090/S0002-9939-1990-1036987-X

States on $W^ *$-algebras and orthogonal vector measures
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Proc. Amer. Math. Soc. 110 (1990), 803-806 Request permission

Abstract:

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 $[1,7]$. Particularly, it allows us to find a simple formula for the transition probability between two states on $\mathcal {A}$ $[3,8]$.

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