Observables on lexicographic effect algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73597648" target="_blank" >RIV/61989592:15310/19:73597648 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs00012-019-0628-y" target="_blank" >https://link.springer.com/article/10.1007%2Fs00012-019-0628-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00012-019-0628-y" target="_blank" >10.1007/s00012-019-0628-y</a>

Result language
angličtina
Original language name
Observables on lexicographic effect algebras
Original language description
We study lexicographic effect algebras which are intervals in lexicographic products H×→G, where (H, u) is a unital po-group and G is a monotone σ-complete po-group with interpolation. We prove that there is a one-to-one correspondence between observables, which are a special kind of σ-homomorphisms and analogues of measurable functions, and spectral resolutions which are systems { xt: t∈ R} of elements of a lexicographic effect algebra that are monotone, “left continuous”, and going to 0 if t→ - ∞ and to 1 if t→ + ∞. We show that this correspondence in lexicographic effect algebras holds only for spectral resolutions with the finiteness property. Otherwise, they do not determine any observable. Whence, the information involved in a spectral resolution with the finiteness property completely describes information about an observable.
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
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OECD FORD branch
10101 - Pure mathematics

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

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