论文标题
提升，$ n $维光谱分辨率和$ n $二维可观察力
Lifting, $n$-Dimensional Spectral Resolutions, and $n$-Dimensional Observables
论文作者
论文摘要
我们表明，在某些自然条件下，我们能够将$ n $维的光谱分辨率从一个单调$σ$ complete Unital po-group提升为另一个单调的complete unital po-group，而第一个是第二个$σ$ - 正态图像。我们注意到，$ n $维频谱分辨率是从$ \ mathbb r^n $映射到一个单调的量子结构，左持续增量，如果一个变量为$ - \ infty $，则将$ 0 $ $ 0 $，如果所有变量为$ 1 $，则$ 1 $ to $ 1 $ to $ 1 $ to $+\ fefty $+elfty $+elfty $。将此结果应用于包括MV-Elgebras在内的一些重要类别的代数类别，我们表明，$ n $维频谱分辨率与$ n $ n $维代数之间有一对一的对应关系，这些效应代数是$σ$ - homomorphismss the bot $ n n of tonten $ -almorphists $ note $ -almorphists $ -almorphists $ -almorphent $ -almorphe $ -Al $ -Al $ -Al $ -Al $ -Al $ -Albb ra f。一个重要的使用工具是loomis-sikorski定理的两种形式，它们使用两种模糊集的部落。此外，我们表明我们可以定义三种$ n $ n $ n $一维可观测值的三种不同类型的$ n $维置。
We show that under some natural conditions, we are able to lift an $n$-dimensional spectral resolution from one monotone $σ$-complete unital po-group into another one, when the first one is a $σ$-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 $σ$-homomorphisms from the Borel $σ$-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.
