Regular states and countable additivity on quantum logics
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- by Anatolij Dvurečenskij, Tibor Neubrunn and Sylvia Pulmannová
- Proc. Amer. Math. Soc. 114 (1992), 931-938
- DOI: https://doi.org/10.1090/S0002-9939-1992-1045591-0
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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.References
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Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 931-938
- MSC: Primary 46C99; Secondary 28A60, 46N50, 81P10
- DOI: https://doi.org/10.1090/S0002-9939-1992-1045591-0
- MathSciNet review: 1045591