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 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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Acknowledgements
The author is very indebted to anonymous referees for their careful reading and suggestions which helped us to improve the readability of the paper. This study was funded by the Grants VEGA Nos. 2/0069/16 SAV and GAČR 15-15286S.
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Communicated by A. Di Nola.
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Dvurečenskij, A. Sum of observables on MV-effect algebras. Soft Comput 22, 2485–2493 (2018). https://doi.org/10.1007/s00500-017-2741-1
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DOI: https://doi.org/10.1007/s00500-017-2741-1