Vigier's theorem for the spectral order and its applications

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F19%3A00332993" target="_blank" >RIV/68407700:21230/19:00332993 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2019.04.016" target="_blank" >https://doi.org/10.1016/j.jmaa.2019.04.016</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2019.04.016" target="_blank" >10.1016/j.jmaa.2019.04.016</a>

Result language
angličtina
Original language name
Vigier's theorem for the spectral order and its applications
Original language description
The paper mainly deals with suprema and infima of self-adjoint operators in a von Neumann algebra M with respect to the spectral order. Let M-sa be the self-adjoint part of M and let <= be the spectral order on M-sa. We show that a decreasing net in (M-sa, <=) with a lower bound has the infimum equal to the strong operator limit. The similar statement is proved for an increasing net bounded above in (M-sa, <=) This version of Vigier's theorem for the spectral order is used to describe suprema and infima of nonempty bounded sets of self-adjoint operators in terms of the strong operator limit and operator means. As an application of our results on suprema and infima, we study the order topology on M-sa, with respect to the spectral order. We show that it is finer than the restriction of the Mackey topology.
Czech name
—
Czech description
—

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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)