Jordan Invariants of Von Neumann Algebras Given by Abelian Subalgebras and Choquet Order on State Spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00350267" target="_blank" >RIV/68407700:21230/21:00350267 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10773-019-04157-w" target="_blank" >https://doi.org/10.1007/s10773-019-04157-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-019-04157-w" target="_blank" >10.1007/s10773-019-04157-w</a>

Result language
angličtina
Original language name
Jordan Invariants of Von Neumann Algebras Given by Abelian Subalgebras and Choquet Order on State Spaces
Original language description
New complete invariants for Jordan parts of von Neumann algebras are presented. We shall prove that the poset of all finite dimensional abelian von Neumann subalgebras ordered by set theoretic inclusion is a complete Jordan invariant for von Neumann algebras. On the other hand, we exhibit an example showing that not any order isomorphism on this structure is derived from a Jordan isomorphism. We apply our results to the Choquet order of orthogonal measures on state spaces of von Neumann algebras. Among others we show that the poset of decompositions of a fixed faithful normal state on a von Neumann algebra endowed with the Choquet order is a complete Jordan invariant for sigma-finite von Neumann algebras.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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