Dye's Theorem and Gleason's Theorem for AW*-algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F15%3A00229788" target="_blank" >RIV/68407700:21230/15:00229788 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2014.09.040" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2014.09.040</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2014.09.040" target="_blank" >10.1016/j.jmaa.2014.09.040</a>

Result language
angličtina
Original language name
Dye's Theorem and Gleason's Theorem for AW*-algebras
Original language description
We prove that any map between projection lattices of AW*-algebras A and B, where A has no Type I-2 direct summand, that preserves orthocomplementation and suprema of arbitrary elements, is a restriction of a normal Jordan *-homomorphism between A and B.This allows us to generalize Dye's Theorem from von Neumann algebras to AW*-algebras. We show that Mackey-Gleason-Bunce-Wright Theorem can be extended to homogeneous AW*-algebras of Type I. The interplay between Dye's Theorem and Gleason's Theorem is shown. As an application we prove that Jordan *-homomorphisms are commutatively determined. Another corollary says that Jordan parts of AW*-algebras can be reconstructed from posets of their abelian subalgebras.
Czech name
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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
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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
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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