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arXiv · 1610.03726

Sum of Observables on MV-Effect Algebras

Anatolij Dvurečenskij
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Abstract

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 and 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.

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Anatolij Dvurečenskij. 2016-10-11. Sum of Observables on MV-Effect Algebras. https://doi.org/10.1007/s10773-017-3472-x

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