Isomorphisms of ordered structures of abelian C-subalgebras of C-algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00182388" target="_blank" >RIV/68407700:21230/11:00182388 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2011.05.035" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2011.05.035</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2011.05.035" target="_blank" >10.1016/j.jmaa.2011.05.035</a>

Result language
angličtina
Original language name
Isomorphisms of ordered structures of abelian C*-subalgebras of C*-algebras
Original language description
The aim of this note is to study the interplay between the Jordan structure of C*-algebra and the structure of its abelian C*-subalgebras. Let Abel(A) be a system of unital C*-subalgebras of a unital C*-algebra A ordered by set theoretic inclusion. We show that any order isomorphism phi : Abel(A) -> Abel(B) can be uniquely written in the form phi(C) = psi(C(sa)) + i psi (C(sa)), where psi is a partially linear Jordan isomorphism between self-adjoint parts of unital C*-algebras A and B. As a corollary weobtain that for certain class of C*-algebras (including von Neumann algebras) ordered structure of abelian subalgebras completely determines the Jordan structure. The results extend hitherto known results for abelian C*-algebras and may be relevant to foundations of quantum theory. (C) 2011 Elsevier Inc. All rights reserved.
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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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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