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- W3008808791 abstract "We show that under some natural conditions, we are able to lift an $n$-dimensional spectral resolution from one monotone $sigma$-complete unital po-group into another one, when the first one is a $sigma$-homomorphic image of the second one. We note that an $n$-dimensional spectral resolution is a mapping from $mathbb R^n$ into a quantum structure which is monotone, left-continuous with non-negative increments and which is going to $0$ if one variable goes to $-infty$ and it goes to $1$ if all variables go to $+infty$. Applying this result to some important classes of effect algebras including also MV-algebras, we show that there is a one-to-one correspondence between $n$-dimensional spectral resolutions and $n$-dimensional observables on these effect algebras which are a kind of $sigma$-homomorphisms from the Borel $sigma$-algebra of $mathbb R^n$ into the quantum structure. An important used tool are two forms of the Loomis--Sikorski theorem which use two kinds of tribes of fuzzy sets. In addition, we show that we can define three different kinds of $n$-dimensional joint observables of $n$ one-dimensional observables." @default.
- W3008808791 created "2020-03-06" @default.
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- W3008808791 date "2020-02-19" @default.
- W3008808791 modified "2023-09-27" @default.
- W3008808791 title "Lifting, $n$-Dimensional Spectral Resolutions, and $n$-Dimensional Observables" @default.
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