Quantum logic and operational quantum mechanics. (English) Zbl 0569.03027
We characterize the class of the \(\mu\)-complete F-spaces with unit corresponding to the observables of a quantum logic. We show that, conversely, every \(\mu\)-complete F-space satisfying certain axioms corresponds to a quantum logic. The latter class of F-spaces generalizes that of ”spectral F-spaces” introduced by E. M. Alfsen and F. W. Shultz and by C. M. Edwards.
MSC:
| 03G12 | Quantum logic |
| 46A40 | Ordered topological linear spaces, vector lattices |
| 81P10 | Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) |
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