A connection between propositional systems in Hilbert spaces and von Neumann algebras
نویسنده
چکیده
A theorem of Bade proves that for a complete Boolean sublattice S£ of 3>(3if) the following holds: SS {PeS£"; P is orthogonal projection operator} We prove that this theorem does not hold for the physically interesting class of non-Boolean propositional systems embedded in a 3>(3if); we derive however a necessary and sufficient condition under which the theorem does hold. This condition is automatically satisfied if the propositional system is Boolean.
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