COMPLETENESS OF GELFAND-NEUMARK-SEGAL INNER PRODUCT SPACE ON JORDAN ALGEBRAS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00303955" target="_blank" >RIV/68407700:21230/16:00303955 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1515/ms-2015-0150" target="_blank" >http://dx.doi.org/10.1515/ms-2015-0150</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2015-0150" target="_blank" >10.1515/ms-2015-0150</a>

Result language
angličtina
Original language name
COMPLETENESS OF GELFAND-NEUMARK-SEGAL INNER PRODUCT SPACE ON JORDAN ALGEBRAS
Original language description
The paper deals with inner product spaces generated by states on Jordan algebras. We show an interplay between completeness of the Gelfand-Neumark-Segal representation space, geometric properties of states on Jordan algebras, structure of irreducible Jordan representations, and properties of normal states on second duals of Jordan algebras. We prove that if the GNS representation space is complete, then given state must be a convex combination of pure states. On the other hand, we analyze structure of inner product spaces arising from states on spin factors and Type In, n = 4, factors, showing their completeness as a consequence. (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
—

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)

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

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