Jan Paseka

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math.RA2025

Dagger categories of orthosets and the complex Hilbert spaces

Jan Paseka, Thomas Vetterlein

An orthoset is a non-empty set $X$ together with a symmetric binary relation $⊥$ and a constant $0$ such that $x \neq ⊥ x$ for any $x \neq = 0$ , and $0 ⊥ x$ for any $x$ . M…

math.RA2025

Characterisation of quadratic spaces over the Hilbert field by means of the orthogonality relation

Miroslav KorbelÃ¡Å, Jan Paseka, Thomas Vetterlein

An orthoset is a set equipped with a symmetric, irreflexive binary relation. With any (anisotropic) Hermitian space $H$ , we may associate the orthoset $(P (H), ⊥)$ , consisting of…

math.RA2025

Adjointable maps between linear orthosets

Jan Paseka, Thomas Vetterlein

Given an (anisotropic) Hermitian space $H$ , the collection $P (H)$ of at most one-dimensional subspaces of $H$ , equipped with the orthogonal relation $⊥$ and the zero linear sub…