On Realization of Partially Ordered Abelian Groups.
The result's identifiers
Result code in 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>
Alternative codes found
RIV/00216224:14310/13:00070761
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On Realization of Partially Ordered Abelian Groups.
Original language description
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
Czech name
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Czech description
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Classification
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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Result continuities
Project
<a href="/en/project/EE2.3.20.0051" target="_blank" >EE2.3.20.0051: Algebraic methods in Quantum Logic</a><br>
Continuities
O - Projekt operacniho programu
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Theoretical Physics
ISSN
0020-7748
e-ISSN
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Volume of the periodical
52
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
2028-2037
UT code for WoS article
000318373700031
EID of the result in the Scopus database
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