Normal orthogonality spaces

J 2022

Normal orthogonality spaces

PASEKA, Jan a Thomas VETTERLEIN

Základní údaje

Originální název

Normal orthogonality spaces

Autoři

PASEKA, Jan (203 Česká republika, garant, domácí) a Thomas VETTERLEIN

Vydání

Journal of Mathematical Analysis and Applications, Elsevier, 2022, 0022-247X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.300

Kód RIV

RIV/00216224:14310/22:00119382

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1016/j.jmaa.2021.125730

UT WoS

000710583300013

EID Scopus

2-s2.0-85116584657

Klíčová slova anglicky

Orthogonality space; Orthoset; Hilbert space; Normal orthogonality space; Boolean subalgebra

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 30. 11. 2021 11:38, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

An orthogonality space is a set X together with a symmetric and irreflexive binary relation ⊥, called the orthogonality relation. A block partition of X is a partition of a maximal set of mutually orthogonal elements of X, and a decomposition of X is a collection of subsets of X each of which is the orthogonal complement of the union of the others. (X, ⊥) is called normal if any block partition gives rise to a unique decomposition of the space. The set of one-dimensional subspaces of a Hilbert space equipped with the usual orthogonality relation provides the motivating example. Together with the maps that are, in a natural sense, compatible with the formation of decompositions from block partitions, the normal orthogonality spaces form a category, denoted by NOS. The objective of the present paper is to characterise both the objects and the morphisms of NOS from various perspectives as well as to compile basic categorical properties of NOS.

Návaznosti

GF20-09869L, projekt VaV

Název: Ortomodularita z různých pohledů

Investor: Grantová agentura ČR, Ortomodularita z různých pohledů, Partnerská agentura (Rakousko)

Citovat

PASEKA, Jan a Thomas VETTERLEIN. Normal orthogonality spaces. Journal of Mathematical Analysis and Applications. Elsevier, 2022, roč. 507, č. 1, s. 125730-125746. ISSN 0022-247X. Dostupné z: https://doi.org/10.1016/j.jmaa.2021.125730.

@article{1806309,
   author = {Paseka, Jan and Vetterlein, Thomas},
   article_number = {1},
   doi = {https://doi.org/10.1016/j.jmaa.2021.125730},
   keywords = {Orthogonality space; Orthoset; Hilbert space; Normal orthogonality space; Boolean subalgebra},
   language = {eng},
   issn = {0022-247X},
   journal = {Journal of Mathematical Analysis and Applications},
   title = {Normal orthogonality spaces},
   url = {https://www.sciencedirect.com/science/article/pii/S0022247X2100809X},
   volume = {507},
   year = {2022}
}

TY  - JOUR
ID  - 1806309
AU  - Paseka, Jan - Vetterlein, Thomas
PY  - 2022
TI  - Normal orthogonality spaces
JF  - Journal of Mathematical Analysis and Applications
VL  - 507
IS  - 1
SP  - 125730
EP  - 125730
PB  - Elsevier
SN  - 0022247X
KW  - Orthogonality space
KW  - Orthoset
KW  - Hilbert space
KW  - Normal orthogonality space
KW  - Boolean subalgebra
UR  - https://www.sciencedirect.com/science/article/pii/S0022247X2100809X
N2  - An orthogonality space is a set X together with a symmetric and irreflexive binary relation ⊥, called the orthogonality relation. A block partition of X is a partition of a maximal set of mutually orthogonal elements of X, and a decomposition of X is a collection of subsets of X each of which is the orthogonal complement of the union of the others. (X, ⊥) is called normal if any block partition gives rise to a unique decomposition of the space. The set of one-dimensional subspaces of a Hilbert space equipped with the usual orthogonality relation provides the motivating example. Together with the maps that are, in a natural sense, compatible with the formation of decompositions from block partitions, the normal orthogonality spaces form a category, denoted by NOS. The objective of the present paper is to characterise both the objects and the morphisms of NOS from various perspectives as well as to compile basic categorical properties of NOS.
ER  -

PASEKA, Jan a Thomas VETTERLEIN. Normal orthogonality spaces. \textit{Journal of Mathematical Analysis and Applications}. Elsevier, 2022, roč.~507, č.~1, s.~125730-125746. ISSN~0022-247X. Dostupné z: https://doi.org/10.1016/j.jmaa.2021.125730.

Přehled o publikaci