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On orders of observables on effect algebras. (English) Zbl 1387.81015
Summary: On the set of bounded observables on an effect algebra, the Olson order defined by spectral resolutions and the standard order defined by a system of \(\sigma\)-additive states are introduced. We show that sharp bounded observables form a Dedekind \(\sigma\)-complete sublattice of a Dedekind complete lattice under the Olson order. In addition, we compare both orders, and we illustrate them on different effect algebras.

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06C15 Complemented lattices, orthocomplemented lattices and posets
46G10 Vector-valued measures and integration
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