论文标题
$ n $二维可观察到$ k $ - 完美的MV-Elgebras和$ k $ - 完美的效应代数。 ii。一对一信件
$n$-dimensional Observables on $k$-Perfect MV-Algebras and $k$-Perfect Effect Algebras. II. One-to-one Correspondence
论文作者
论文摘要
该论文是对$ n $维频谱分辨率和$ n $二维可观察到词素类型的量子结构的一对一的对应关系的研究的延续。在第一部分中，我们介绍了$ n $二维的光谱分辨率和可观察到的主要特性，并且深入研究了对我们的研究至关重要的特征点。在目前的第二部分中，我们的研究有一个主体。我们研究了$ n $二维可观测值与$ n $二维光谱分辨率之间的一对一对应关系，其值是一种词典形式的量子结构，例如完美的MV-Elgebras或Perfect效应代数。该问题的多维版本比一维元素更为复杂，因为如果我们的代数结构为$ k $ $ k> 1 $，那么即使对于频谱分辨率的二维情况，我们也会有更多特征点。获得的结果适用于存在$ n $ n $维的联合观察，可在完美的MV-Algebra上观察到$ n $ n $一维的可观察物，以及$ n $ n $维的可观察力。
The paper is a continuation of the research on a one-to-one correspondence between $n$-dimensional spectral resolutions and $n$-dimensional observables on lexicographic types of quantum structures which started in \cite{DvLa4}. In Part I, we presented the main properties of $n$-dimensional spectral resolutions and observables, and we deeply studied characteristic points which are crucial for our study. In present Part II, there is a main body of our research. We investigate a one-to-one correspondence between $n$-dimensional observables and $n$-dimensional spectral resolutions with values in a kind of a lexicographic form of quantum structures like perfect MV-algebras or perfect effect algebras. The multidimensional version of this problem is more complicated than a one-dimensional one because if our algebraic structure is $k$-perfect for $k>1$, then even for the two-dimensional case of spectral resolutions we have more characteristic points. The obtained results are applied to existence of an $n$-dimensional meet joint observable of $n$ one-dimensional observables on a perfect MV-algebra and a sum of $n$-dimensional observables.
