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Olson order of quantum observables. (English) Zbl 1358.81011
Summary: M. P. Olson [Proc. Am. Math. Soc. 28, 537–544 (1971; Zbl 0215.20504)] showed that the system of effect operators of the Hilbert space can be ordered by the so-called spectral order such that the system of effect operators is a complete lattice. Using his ideas, we introduce a partial order, called the Olson order, on the set of bounded observables of a complete lattice effect algebra. We show that the set of bounded observables is a Dedekind complete lattice.

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G12 Quantum logic
06C15 Complemented lattices, orthocomplemented lattices and posets
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