The spectrum of the sum of observables on sigma-complete MV-effect algebras

• Autoři: JANDA Jiří; XIE Yongjian
• Rok publikování: 2018
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Soft computing
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: Full Text
• Doi: http://dx.doi.org/10.1007/s00500-018-3078-0
• Klíčová slova: Monotone sigma-complete effect algebra; Observable on a sigma-complete MV-effect algebra; Sum of observables; Spectrum of an observable; Sharp observable; Meager observable
• Popis: The natural question about the sum of observables on -complete MV-effect algebras, which was recently defined by A. Dvureenskij, is how it affects spectra of observables, particularly, their extremal points. We describe boundaries for extremal points of the spectrum of the sum of observables in a general case, and we give necessary and sufficient conditions under which the spectrum attains these boundary values. Moreover, we show that every bounded observable x on a complete MV-effect algebra E can be decomposed into the sum is a meager and extremally non-invertible observable.

Související projekty

• Algebraické, vícehodnotové a kvantové struktury pro modelování neurčitosti