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@article{1114273, author = {Janda, Jiří and Riečanová, Zdenka}, article_number = {6}, doi = {http://dx.doi.org/10.1007/s10773-013-1532-4}, keywords = {Effect algebra MV-effect algebrMacNeille completion;Positive linear operators in Hilbert space;Hilbert space effect-representation}, language = {eng}, issn = {0020-7748}, journal = {International Journal of Theoretical Physics}, title = {Extensions of Ordering Sets of States from Effect Algebras onto Their MacNeille Completions}, url = {http://link.springer.com/article/10.1007%2Fs10773-013-1532-4}, volume = {52}, year = {2013} }
TY - JOUR ID - 1114273 AU - Janda, Jiří - Riečanová, Zdenka PY - 2013 TI - Extensions of Ordering Sets of States from Effect Algebras onto Their MacNeille Completions JF - International Journal of Theoretical Physics VL - 52 IS - 6 SP - 2171-2180 EP - 2171-2180 PB - Springer SN - 00207748 KW - Effect algebra MV-effect algebrMacNeille completion;Positive linear operators in Hilbert space;Hilbert space effect-representation UR - http://link.springer.com/article/10.1007%2Fs10773-013-1532-4 L2 - http://link.springer.com/article/10.1007%2Fs10773-013-1532-4 N2 - 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. ER -
JANDA, Jiří and Zdenka RIEČANOVÁ. Extensions of Ordering Sets of States from Effect Algebras onto Their MacNeille Completions. \textit{International Journal of Theoretical Physics}. Springer, 2013, vol.~52, No~6, p.~2171-2180. ISSN~0020-7748. Available from: https://dx.doi.org/10.1007/s10773-013-1532-4.
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