Observables on σ-Frame effect Algebras as Upper Semicontinuous Functions

Jiří Janda

doi:10.1016/S0034-4877(22)00034-9

Observables on σ-Frame effect Algebras as Upper Semicontinuous Functions

Jiří Janda

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We showed that the set of observables O(E) on a σ-frame effect algebra E is in one-to-one correspondence with the set USC(is) of point-free versions of real upper semicontinous functions on the order reduct of E. The Olson order and the sum on O(E) are represented by the usual order and the sum of real upper semicontinuous functions. Sharp observables SO(E) are then described by continuous functions on E and this correspondence is one-to-one in the case when E forms an MV-algebra.

Original language	English
Pages (from-to)	291-306
Journal	Reports on Mathematical Physics
Volume	89
Issue number	3
DOIs	https://doi.org/10.1016/S0034-4877(22)00034-9
Publication status	Published - Jun 2022

OECD Field of Science

1.3 Physical Sciences

Keywords

effect algebra
sum of observables
observable
point-free semicontinuous functions
σ-frame

Access to Document

10.1016/S0034-4877(22)00034-9

Cite this

@article{29b86acc01014cb29b7aeb9ec5d651b3,

title = "Observables on σ-Frame effect Algebras as Upper Semicontinuous Functions",

abstract = "We showed that the set of observables O(E) on a σ-frame effect algebra E is in one-to-one correspondence with the set USC(is) of point-free versions of real upper semicontinous functions on the order reduct of E. The Olson order and the sum on O(E) are represented by the usual order and the sum of real upper semicontinuous functions. Sharp observables SO(E) are then described by continuous functions on E and this correspondence is one-to-one in the case when E forms an MV-algebra.",

keywords = "effect algebra, sum of observables, observable, point-free semicontinuous functions, σ-frame",

author = "Ji{\v r}{\'i} Janda",

note = "Publisher Copyright: {\textcopyright} 2022 Polish Scientific Publishers",

year = "2022",

month = jun,

doi = "10.1016/S0034-4877(22)00034-9",

language = "English",

volume = "89",

pages = "291--306",

journal = "Reports on Mathematical Physics",

issn = "0034-4877",

publisher = "Elsevier Ltd",

number = "3",

}

TY - JOUR

T1 - Observables on σ-Frame effect Algebras as Upper Semicontinuous Functions

AU - Janda, Jiří

PY - 2022/6

Y1 - 2022/6

N2 - We showed that the set of observables O(E) on a σ-frame effect algebra E is in one-to-one correspondence with the set USC(is) of point-free versions of real upper semicontinous functions on the order reduct of E. The Olson order and the sum on O(E) are represented by the usual order and the sum of real upper semicontinuous functions. Sharp observables SO(E) are then described by continuous functions on E and this correspondence is one-to-one in the case when E forms an MV-algebra.

AB - We showed that the set of observables O(E) on a σ-frame effect algebra E is in one-to-one correspondence with the set USC(is) of point-free versions of real upper semicontinous functions on the order reduct of E. The Olson order and the sum on O(E) are represented by the usual order and the sum of real upper semicontinuous functions. Sharp observables SO(E) are then described by continuous functions on E and this correspondence is one-to-one in the case when E forms an MV-algebra.

KW - effect algebra

KW - sum of observables

KW - observable

KW - point-free semicontinuous functions

KW - σ-frame

UR - https://www.sciencedirect.com/science/article/pii/S0034487722000349

UR - https://www.scopus.com/pages/publications/85133210688

U2 - 10.1016/S0034-4877(22)00034-9

DO - 10.1016/S0034-4877(22)00034-9

M3 - Article

SN - 0034-4877

VL - 89

SP - 291

EP - 306

JO - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

IS - 3

ER -

Observables on σ-Frame effect Algebras as Upper Semicontinuous Functions

Abstract

OECD Field of Science

Keywords

Access to Document

Other files and links

Fingerprint

Cite this