Spectral order isomorphisms and AW*-factors

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00359538" target="_blank" >RIV/68407700:21230/22:00359538 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/mana.202000043" target="_blank" >https://doi.org/10.1002/mana.202000043</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.202000043" target="_blank" >10.1002/mana.202000043</a>

Result language
angličtina
Original language name
Spectral order isomorphisms and AW*-factors
Original language description
The paper deals with spectral order isomorphisms in the framework of AW*-algebras. We establish that every spectral order isomorphism between sets of all self-adjoint elements (or between sets of all effects, or between sets of all positive elements) in AW*-factors of Type I has a canonical form induced by a continuous function calculus and an isomorphism between projection lattices. In particular, this solves an open question about spectral order automorphisms of the set of all (bounded) self-adjoint operators on an infinite-dimensional Hilbert space. We also discuss spectral order isomorphisms preserving, in addition, orthogonality in both directions.
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
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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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