Adjointable maps between linear orthosets

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Adjointable maps between linear orthosets
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF25-20013L" target="_blank" >GF25-20013L: Orthogonality and Symmetry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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