Observables on lexicographic effect algebras

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Observables on lexicographic effect algebras

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Observables on lexicographic effect algebras

Popis výsledku anglicky

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.

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

2019

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

80

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

22

Strana od-do

"49-1"-"49-22"

Kód UT WoS článku

000508562100002

EID výsledku v databázi Scopus

2-s2.0-85075125496