Decompositions of preduals of JBW and JBW* algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10366376" target="_blank" >RIV/00216208:11320/17:10366376 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21230/17:00306584
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2016.08.031" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2016.08.031</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2016.08.031" target="_blank" >10.1016/j.jmaa.2016.08.031</a>

Result language
angličtina
Original language name
Decompositions of preduals of JBW and JBW* algebras
Original language description
We prove that the predual of any JBW*-algebra is a complex 1-Plichko space and the predual of any JBW-algebra is a real 1-Plichko space. I.e., any such space has a countably 1-norming Markushevich basis, or, equivalently, a commutative 1-projectional skeleton. This extends recent results of the authors who proved the same for preduals of von Neumann algebras and their self-adjoint parts. However, the more general setting of Jordan algebras turned to be much more complicated. We use in the proof a set-theoretical method of elementary submodels. As a byproduct we obtain a result on amalgamation of projectional skeletons.
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
—
OECD FORD branch
10101 - Pure mathematics

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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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