Orthogonal Measures on State Spaces and Context Structure of Quantum Theory
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00300844" target="_blank" >RIV/68407700:21230/16:00300844 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10773-016-2964-4" target="_blank" >http://dx.doi.org/10.1007/s10773-016-2964-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-016-2964-4" target="_blank" >10.1007/s10773-016-2964-4</a>
Alternative languages
Result language
angličtina
Original language name
Orthogonal Measures on State Spaces and Context Structure of Quantum Theory
Original language description
An interplay between recent topos theoretic approach and standard convex theoretic approach to quantum theory is discovered. Combining new results on isomorphisms of posets of all abelian subalgebras of von Neumann algebras with classical Tomita's theorem from state space Choquet theory, we show that order isomorphisms between the sets of orthogonal measures (resp. finitely supported orthogonal measures) on state spaces endowed with the Choquet order are given by Jordan au-isomorphims between corresponding operator algebras. It provides new complete Jordan invariants for sigma-finite von Neumann algebras in terms of decompositions of states and shows that one can recover physical system from associated structure of convex decompositions (discrete or continuous) of a fixed state.
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/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
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
55
Issue of the periodical within the volume
7
Country of publishing house
US - UNITED STATES
Number of pages
13
Pages from-to
3353-3365
UT code for WoS article
000378746600027
EID of the result in the Scopus database
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