Quantum logics with the Radon-Nikodym property |
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Authors: | Mirko Navara Pavel Pták |
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Institution: | (1) Department of Mathematics, Faculty of Electrical Engineering, Technical University of Prague, 16627 Prague, Czechoslovakia |
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Abstract: | Following the definition of S. Gudder and J. Zerbe, we say that a logicL has the Radon-Nikodym property (or, in short,L is an RN logic) if the following condition holds: Ifs, t are states onL ands is absolutely continuous with respect tot, then there is a central observablex such that
for allaL. We first consider general RN logics. We establish their basic properties and show that they are closed under the formation of epimorphisms and products. Then we take up the RN property for concrete logics. We first show that in many cases the concrete RN logics have to be fully compatible (= Boolean -algebras). In contrast to that, we show that there are concrete RN logics with an arbitrary degree of noncompatibility. This extends the result of Navara and Pták and answers in full the question posed by Gudder and Zerbe. |
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Keywords: | Primary: 81B10 secondary: 03G12 28A25 |
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