Adjointable maps between linear orthosets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144313" target="_blank" >RIV/00216224:14310/25:00144313 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jmaa.2025.129494" target="_blank" >https://doi.org/10.1016/j.jmaa.2025.129494</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2025.129494" target="_blank" >10.1016/j.jmaa.2025.129494</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Adjointable maps between linear orthosets

Popis výsledku v původním jazyce

Given an (anisotropic) Hermitian space H, the collection P(H) of at most onedimensional subspaces of H, equipped with the orthogonal relation perpendicular to and the zero linear subspace {0}, is a linear orthoset and up to orthoisomorphism any linear orthoset of rank &gt;= 4 arises in this way. We investigate in this paper the correspondence of structure-preserving maps between Hermitian spaces on the one hand and between the associated linear orthosets on the other hand. Our particular focus is on adjointable maps. We show that, under a mild assumption, adjointable maps between linear orthosets are induced by quasilinear maps between Hermitian spaces and if the latter are linear, they are adjointable as well. Specialised versions of this correlation lead to Wigner-type theorems; we see, for instance, that orthoisomorphisms between the orthosets associated with at least 3-dimensional Hermitian spaces are induced by quasiunitary maps. In addition, we point out that orthomodular spaces of dimension &gt;= 4 can be characterised as irreducible Fr &amp; eacute;chet orthosets such that the inclusion map of any subspace is adjointable. Together with a transitivity condition, we may in this way describe the infinite-dimensional classical Hilbert spaces.

Název v anglickém jazyce

Adjointable maps between linear orthosets

Popis výsledku anglicky

Given an (anisotropic) Hermitian space H, the collection P(H) of at most onedimensional subspaces of H, equipped with the orthogonal relation perpendicular to and the zero linear subspace {0}, is a linear orthoset and up to orthoisomorphism any linear orthoset of rank &gt;= 4 arises in this way. We investigate in this paper the correspondence of structure-preserving maps between Hermitian spaces on the one hand and between the associated linear orthosets on the other hand. Our particular focus is on adjointable maps. We show that, under a mild assumption, adjointable maps between linear orthosets are induced by quasilinear maps between Hermitian spaces and if the latter are linear, they are adjointable as well. Specialised versions of this correlation lead to Wigner-type theorems; we see, for instance, that orthoisomorphisms between the orthosets associated with at least 3-dimensional Hermitian spaces are induced by quasiunitary maps. In addition, we point out that orthomodular spaces of dimension &gt;= 4 can be characterised as irreducible Fr &amp; eacute;chet orthosets such that the inclusion map of any subspace is adjointable. Together with a transitivity condition, we may in this way describe the infinite-dimensional classical Hilbert spaces.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure 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

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

550

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

1-19

Kód UT WoS článku

001455459900001

EID výsledku v databázi Scopus

2-s2.0-105000602657