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Sum of observables on MV-effect algebras. (English) Zbl 1398.06012
Summary: Using a one-to-one correspondence between observables and their spectral resolutions, we introduce the sum of any two bounded observables of a \(\sigma\)-MV-effect algebra. This sum is commutative, associative with neutral element. Under the Olson order of observables, the set of bounded observables is a partially ordered semigroup, and the set of sharp observables is even a Dedekind \(\sigma\)-complete \(\ell\)-group with strong unit.

MSC:
06D35 MV-algebras
03G12 Quantum logic
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