Extensions of Ordering Sets of States from Effect Algebras onto Their MacNeille Completions
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Theoretical Physics |
| MU Faculty or unit | |
| Citation | |
| Web | http://link.springer.com/article/10.1007%2Fs10773-013-1532-4 |
| Doi | http://dx.doi.org/10.1007/s10773-013-1532-4 |
| Field | General mathematics |
| Keywords | Effect algebra MV-effect algebrMacNeille completion;Positive linear operators in Hilbert space;Hilbert space effect-representation |
| Description | In "Riečanová Z, Zajac M.: Hilbert Space Effect-Representations of Effect Algebras" it was shown that an effect algebra $E$ with an ordering set ${\cal M}$ of states can by embedded into a Hilbert space effect algebra ${\cal E}(l_2({\cal M}))$. We consider the problem when its effect algebraic MacNeille completion $\hat{E}$ can be also embedded into the same Hilbert space effect algebra ${\cal E}(l_2({\cal M}))$. That is when the ordering set $\cal M$ of states on $E$ can be be extended to an ordering set of states on $\hat{E}$. We give an answer for all Archimedean MV-effect algebras and Archimedean atomic lattice effect algebras. |
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