ON REALIZATION OF EFFECT ALGEBRAS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F16%3A00088581" target="_blank" >RIV/00216224:14310/16:00088581 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1515/ms-2015-0140" target="_blank" >http://dx.doi.org/10.1515/ms-2015-0140</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2015-0140" target="_blank" >10.1515/ms-2015-0140</a>

Result language
angličtina
Original language name
ON REALIZATION OF EFFECT ALGEBRAS
Original language description
A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not order embeddable into the standard quantum logic, the lattice L(H) of all closed subspaces of a separable complex Hilbert space. We show that a finite generalized effect algebra is order embeddable into the standard effect algebra E(H) of effects of a separable complex Hilbert space iff it has an order determining set of generalized states iff it is order embeddable into the power of a finite MV-chain. As an application we obtain an algorithm, which is based on the simplex algorithm, deciding whether such an order embedding exists and, if the answer is positive, constructing it. (C) 2016 Mathematical Institute Slovak Academy of Sciences
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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