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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 a Zdenka RIEČANOVÁ. Extensions of Ordering Sets of States from Effect Algebras onto Their MacNeille Completions. \textit{International Journal of Theoretical Physics}. Springer, 2013, roč.~52, č.~6, s.~2171-2180. ISSN~0020-7748. Dostupné z: https://dx.doi.org/10.1007/s10773-013-1532-4.
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