Two-Dimensional Observables and Spectral Resolutions

Kód výsledku v IS VaVaI

RIV/61989592:15310/20:73603669 - isvavai.cz

Výsledek na webu

https://www.sciencedirect.com/science/article/pii/S0034487720300239

DOI - Digital Object Identifier

10.1016/S0034-4877(20)30023-9

Jazyk výsledku

angličtina

Název v původním jazyce

Two-Dimensional Observables and Spectral Resolutions

Popis výsledku v původním jazyce

A two-dimensional observable is a special kind of a sigma-homomorphism defined on the Borel sigma-algebra of the real plane with values in a sigma-complete MV-algebra or in a monotone sigma-complete effect algebra. A two-dimensional spectral resolution is a mapping defined on the real plane with values in a sigma-complete MV-algebra or in a monotone sigma-complete effect algebra which has properties similar to a two-dimensional distribution function in probability theory. We show that there is a one-to-one correspondence between two-dimensional observables and two-dimensional spectral resolutions defined on a sigma-complete MV-algebras as well as on the monotone s-complete effect algebras with the Riesz decomposition property. The result is applied to the existence of a joint two-dimensional observable of two one-dimensional observables.

Název v anglickém jazyce

Two-Dimensional Observables and Spectral Resolutions

Popis výsledku anglicky

A two-dimensional observable is a special kind of a sigma-homomorphism defined on the Borel sigma-algebra of the real plane with values in a sigma-complete MV-algebra or in a monotone sigma-complete effect algebra. A two-dimensional spectral resolution is a mapping defined on the real plane with values in a sigma-complete MV-algebra or in a monotone sigma-complete effect algebra which has properties similar to a two-dimensional distribution function in probability theory. We show that there is a one-to-one correspondence between two-dimensional observables and two-dimensional spectral resolutions defined on a sigma-complete MV-algebras as well as on the monotone s-complete effect algebras with the Riesz decomposition property. The result is applied to the existence of a joint two-dimensional observable of two one-dimensional observables.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10303 - Particles and field physics

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

REPORTS ON MATHEMATICAL PHYSICS

ISSN

0034-4877

e-ISSN

—

Svazek periodika

85

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

29

Strana od-do

163-191

Kód UT WoS článku

000528253600001

EID výsledku v databázi Scopus

2-s2.0-85083286780