Adjointable maps between linear orthosets

J 2025

Adjointable maps between linear orthosets

PASEKA, Jan a Thomas VETTERLEIN

Základní údaje

Originální název

Adjointable maps between linear orthosets

Autoři

PASEKA, Jan a Thomas VETTERLEIN

Vydání

Journal of Mathematical Analysis and Applications, San Diego, Elsevier, 2025, 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: 1.200 v roce 2024

Označené pro přenos do RIV

Ano

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Linear orthoset; Hermitian space; Hilbert space; Projective geometry; Semilinear map; Quasilinear map

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 29. 4. 2025 11:31, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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 >= 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 >= 4 can be characterised as irreducible Fr & 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.

Návaznosti

GF25-20013L, projekt VaV

Název: Ortogonalita a symetrie

Investor: Grantová agentura ČR, Ortogonalita a symetrie, Partnerská agentura

Citovat

PASEKA, Jan a Thomas VETTERLEIN. Adjointable maps between linear orthosets. Journal of Mathematical Analysis and Applications. San Diego: Elsevier, 2025, roč. 550, č. 1, s. 1-19. ISSN 0022-247X. Dostupné z: https://doi.org/10.1016/j.jmaa.2025.129494.

@article{2493820,
   author = {Paseka, Jan and Vetterlein, Thomas},
   article_location = {San Diego},
   article_number = {1},
   doi = {https://doi.org/10.1016/j.jmaa.2025.129494},
   keywords = {Linear orthoset; Hermitian space; Hilbert space; Projective geometry; Semilinear map; Quasilinear map},
   language = {eng},
   issn = {0022-247X},
   journal = {Journal of Mathematical Analysis and Applications},
   title = {Adjointable maps between linear orthosets},
   url = {https://doi.org/10.1016/j.jmaa.2025.129494},
   volume = {550},
   year = {2025}
}

TY  - JOUR
ID  - 2493820
AU  - Paseka, Jan - Vetterlein, Thomas
PY  - 2025
TI  - Adjointable maps between linear orthosets
JF  - Journal of Mathematical Analysis and Applications
VL  - 550
IS  - 1
SP  - 1-19
EP  - 1-19
PB  - Elsevier
SN  - 0022247X
KW  - Linear orthoset
KW  - Hermitian space
KW  - Hilbert space
KW  - Projective geometry
KW  - Semilinear map
KW  - Quasilinear map
UR  - https://doi.org/10.1016/j.jmaa.2025.129494
N2  - 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 >= 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 >= 4 can be characterised as irreducible Fr & 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.
ER  -

PASEKA, Jan a Thomas VETTERLEIN. Adjointable maps between linear orthosets. \textit{Journal of Mathematical Analysis and Applications}. San Diego: Elsevier, 2025, roč.~550, č.~1, s.~1-19. ISSN~0022-247X. Dostupné z: https://doi.org/10.1016/j.jmaa.2025.129494.

Přehled o publikaci