On the observables on quantum logics |
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Authors: | S. Pulmannová |
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Affiliation: | (1) Institute for Measurement and Measurement Technique of the Slovak Academy of Sciences, Bratislava, Czechoslovakia |
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Abstract: | Two postulates concerning observables on a quantum logic are formulated. By Postulate 1 compatibility of observables is defined by the strong topology on the set of observables. Postulate 2 requires that the range of the sum of observables ought to be contained in the smallestC-closed sublogic generated by their ranges. It is shown that the Hilbert space logicL(H) satisfies the two postulates. A theorem on the connection between joint distributions of types 1 and 2 on the logic satisfying Postulate 2 is proved. |
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