Sum of Observables on MV-Effect Algebras

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.

References in corpus (6)

• Sharp and fuzzy observables on effect algebras
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• Blocks of homogeneous effect algebras
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• Olson Order of Quantum Observables
• Quantum Observables and Effect Algebras

Cited by in corpus (1)

• Quantum Observables and Effect Algebras