Categories of Orthosets and Adjointable Maps

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144414" target="_blank" >RIV/00216224:14310/25:00144414 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10773-025-06031-4" target="_blank" >https://link.springer.com/article/10.1007/s10773-025-06031-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10773-025-06031-4" target="_blank" >10.1007/s10773-025-06031-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Categories of Orthosets and Adjointable Maps

Popis výsledku v původním jazyce

An orthoset is a non-empty set together with a symmetric and irreflexive binary relation perp, called the orthogonality relation. An orthoset with 0 is an orthoset augmented with an additional element 0, called falsity, which is orthogonal to every element. The collection of subspaces of a Hilbert space that are spanned by a single vector provides a motivating example. We say that a map f :X rightarrow Y between orthosets with 0 possesses the adjoint g :Y rightarrow X if, for any x in X and y in Y, f(x) perp y if and only if x perp g(y). We call f in this case adjointable. For instance, any bounded linear map between Hilbert spaces induces a map with this property. We discuss in this paper adjointability from several perspectives and we put a particular focus on maps preserving the orthogonality relation. We moreover investigate the category mathcal{O}mathcal{S} of all orthosets with 0 and adjointable maps between them. We especially focus on the full subcategory mathcalligra {i}mathcal{O}mathcal{S} of irredundant orthosets with 0. mathcalligra {i}mathcal{O}mathcal{S}can be made into a dagger category, the dagger of a morphism being its unique adjoint. mathcalligra {i}mathcal{O}mathcal{S} contains dagger subcategories of various sorts and provides in particular a framework for the investigation of Hilbert spaces.

Název v anglickém jazyce

Categories of Orthosets and Adjointable Maps

Popis výsledku anglicky

An orthoset is a non-empty set together with a symmetric and irreflexive binary relation perp, called the orthogonality relation. An orthoset with 0 is an orthoset augmented with an additional element 0, called falsity, which is orthogonal to every element. The collection of subspaces of a Hilbert space that are spanned by a single vector provides a motivating example. We say that a map f :X rightarrow Y between orthosets with 0 possesses the adjoint g :Y rightarrow X if, for any x in X and y in Y, f(x) perp y if and only if x perp g(y). We call f in this case adjointable. For instance, any bounded linear map between Hilbert spaces induces a map with this property. We discuss in this paper adjointability from several perspectives and we put a particular focus on maps preserving the orthogonality relation. We moreover investigate the category mathcal{O}mathcal{S} of all orthosets with 0 and adjointable maps between them. We especially focus on the full subcategory mathcalligra {i}mathcal{O}mathcal{S} of irredundant orthosets with 0. mathcalligra {i}mathcal{O}mathcal{S}can be made into a dagger category, the dagger of a morphism being its unique adjoint. mathcalligra {i}mathcal{O}mathcal{S} contains dagger subcategories of various sorts and provides in particular a framework for the investigation of Hilbert spaces.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/GF25-20013L" target="_blank" >GF25-20013L: Ortogonalita a symetrie</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

International Journal of Theoretical Physics

ISSN

0020-7748

e-ISSN

1572-9575

Svazek periodika

64

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

1-28

Kód UT WoS článku

001497138300002

EID výsledku v databázi Scopus

2-s2.0-105006928506