Lifting,n-dimensional spectral resolutions, andn-dimensional observables

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603663" target="_blank" >RIV/61989592:15310/20:73603663 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs00012-020-00664-8" target="_blank" >https://link.springer.com/article/10.1007%2Fs00012-020-00664-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00012-020-00664-8" target="_blank" >10.1007/s00012-020-00664-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Lifting,n-dimensional spectral resolutions, andn-dimensional observables

Popis výsledku v původním jazyce

We show that under some natural conditions, we are able to lift an n-dimensional spectral resolution from one monotone sigma-complete unital po-group into another one, when the first one is a sigma-homomorphic image of the second one. We note that an n-dimensional spectral resolution is a mapping from R-n into a quantum structure which is monotone, left-continuous with non-negative increments and which is going to 0 if one variable goes to -infinity and it goes to 1 if all variables go to +infinity. Applying this result to some important classes of effect algebras including also MV-algebras, we show that there is a one-to-one correspondence between n-dimensional spectral resolutions and n-dimensional observables on these effect algebras which are a kind of sigma-homomorphisms from the Borel sigma-algebra of R-n into the quantum structure. An important used tool are two forms of the Loomis-Sikorski theorem which use two kinds of tribes of fuzzy sets. In addition, we show that we can define three different kinds of n-dimensional joint observables of n one-dimensional observables.

Název v anglickém jazyce

Lifting,n-dimensional spectral resolutions, andn-dimensional observables

Popis výsledku anglicky

We show that under some natural conditions, we are able to lift an n-dimensional spectral resolution from one monotone sigma-complete unital po-group into another one, when the first one is a sigma-homomorphic image of the second one. We note that an n-dimensional spectral resolution is a mapping from R-n into a quantum structure which is monotone, left-continuous with non-negative increments and which is going to 0 if one variable goes to -infinity and it goes to 1 if all variables go to +infinity. Applying this result to some important classes of effect algebras including also MV-algebras, we show that there is a one-to-one correspondence between n-dimensional spectral resolutions and n-dimensional observables on these effect algebras which are a kind of sigma-homomorphisms from the Borel sigma-algebra of R-n into the quantum structure. An important used tool are two forms of the Loomis-Sikorski theorem which use two kinds of tribes of fuzzy sets. In addition, we show that we can define three different kinds of n-dimensional joint observables of n one-dimensional observables.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

ALGEBRA UNIVERSALIS

ISSN

0002-5240

e-ISSN

—

Svazek periodika

81

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

36

Strana od-do

34

Kód UT WoS článku

000540174600001

EID výsledku v databázi Scopus

2-s2.0-85086357532