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

 

Regular states and countable additivity on quantum logics


Authors: Anatolij Dvurečenskij, Tibor Neubrunn and Sylvia Pulmannová
Journal: Proc. Amer. Math. Soc. 114 (1992), 931-938
MSC: Primary 46C99; Secondary 28A60, 46N50, 81P10
MathSciNet review: 1045591
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Abstract: We give a counterexample of the result of Béaver and Cook concerning a generalization of the Alexandroff theorem for regular, finitely-additive states on quantum logics using states on the system of all splitting subspaces of an incomplete inner-product space. Moreover, we introduce another type of state regularity which entails countable additivity of states on logics.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1045591-0
PII: S 0002-9939(1992)1045591-0
Keywords: Quantum logic, state, regular state, countable additivity, inner product space, splitting subspace
Article copyright: © Copyright 1992 American Mathematical Society