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Enlargements of quantum logics. (English) Zbl 0617.06006

Let K be a quantum logic whose state space is nonvoid. Let B be a Boolean algebra and let C be a compact convex subset of a locally convex topological linear space. Then K can be embedded into a logic L such that the centre of L equals B and the state space of L equals C. (The result remains valid when we replace the word ”logic” with ”orthomodular lattice”.)

MSC:

06C15 Complemented lattices, orthocomplemented lattices and posets
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G12 Quantum logic
46L30 States of selfadjoint operator algebras
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