On Realization of Partially Ordered Abelian Groups.
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F13%3A33145904" target="_blank" >RIV/61989592:15310/13:33145904 - isvavai.cz</a>
Nalezeny alternativní kódy
RIV/00216224:14310/13:00070761
Výsledek na webu
<a href="http://dx.doi.org/10.1007/s10773-012-1426-x" target="_blank" >http://dx.doi.org/10.1007/s10773-012-1426-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-012-1426-x" target="_blank" >10.1007/s10773-012-1426-x</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
On Realization of Partially Ordered Abelian Groups.
Popis výsledku v původním jazyce
The paper is devoted to algebraic structures connected with the logic of quantum mechanics. Since every (generalized) effect algebra with an order determining set of (generalized) states can be represented by means of an abelian partially ordered group and events in quantum mechanics can be described by positive operators in a suitable Hilbert space, we are focused in a representation of partially ordered abelian groups by means of sets of suitable linear operators. We show that there is a set of pointsseparating R-maps on a given partially ordered abelian group G if and only if there is an injective non-trivial homomorphism of G to the symmetric operators on a dense set in a complex Hilbert space H which is equivalent to an existence of an injectivenon-trivial homomorphism of G into a certain power of R. A similar characterization is derived for an order determining set of R-maps and symmetric operators on a dense set in a complex Hilbert space H . We also characterize effect algebr
Název v anglickém jazyce
On Realization of Partially Ordered Abelian Groups.
Popis výsledku anglicky
The paper is devoted to algebraic structures connected with the logic of quantum mechanics. Since every (generalized) effect algebra with an order determining set of (generalized) states can be represented by means of an abelian partially ordered group and events in quantum mechanics can be described by positive operators in a suitable Hilbert space, we are focused in a representation of partially ordered abelian groups by means of sets of suitable linear operators. We show that there is a set of pointsseparating R-maps on a given partially ordered abelian group G if and only if there is an injective non-trivial homomorphism of G to the symmetric operators on a dense set in a complex Hilbert space H which is equivalent to an existence of an injectivenon-trivial homomorphism of G into a certain power of R. A similar characterization is derived for an order determining set of R-maps and symmetric operators on a dense set in a complex Hilbert space H . We also characterize effect algebr
Klasifikace
Druh
J<sub>x</sub> - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
CEP obor
BA - Obecná matematika
OECD FORD obor
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Návaznosti výsledku
Projekt
<a href="/cs/project/EE2.3.20.0051" target="_blank" >EE2.3.20.0051: Algebraické metody v kvantové logice</a><br>
Návaznosti
O - Projekt operacniho programu
Ostatní
Rok uplatnění
2013
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
International Journal of Theoretical Physics
ISSN
0020-7748
e-ISSN
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Svazek periodika
52
Číslo periodika v rámci svazku
6
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
10
Strana od-do
2028-2037
Kód UT WoS článku
000318373700031
EID výsledku v databázi Scopus
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