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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

States on $ W\sp *$-algebras and orthogonal vector measures


Author: Jan Hamhalter
Journal: Proc. Amer. Math. Soc. 110 (1990), 803-806
MSC: Primary 81P10; Secondary 46L30
MathSciNet review: 1036987
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1036987-X
PII: S 0002-9939(1990)1036987-X
Article copyright: © Copyright 1990 American Mathematical Society