Spectral order on AW*-algebras and its preservers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00300997" target="_blank" >RIV/68407700:21230/16:00300997 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1134/S1995080216040107" target="_blank" >http://dx.doi.org/10.1134/S1995080216040107</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1134/S1995080216040107" target="_blank" >10.1134/S1995080216040107</a>

Result language
angličtina
Original language name
Spectral order on AW*-algebras and its preservers
Original language description
We study the spectral order on the set of positive contractions in an AW*-algebra. We introduce the concept of lattice theoretic center of the resulting spectral lattice and show that it coincides with the algebraic center of the underlying AW*-algebra A if A is finite. By applying this result we generalize hitherto known characterizations of preserves of the spectral order by showing that any bijection φ acting on the spectral lattice of a finite AW*-algebra that preserves spectral order and orthogonality in both directions is a composition of function calculus and a Jordan *-isomorphism. We show that this result holds in a wide context of all AW*-algebras provided that φ preserves in addition the multiples of unity.
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
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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