Normal orthogonality spaces

Varování

Publikace nespadá pod Ekonomicko-správní fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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PASEKA Jan VETTERLEIN Thomas

Rok publikování 2022
Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Mathematical Analysis and Applications
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://www.sciencedirect.com/science/article/pii/S0022247X2100809X
Doi http://dx.doi.org/10.1016/j.jmaa.2021.125730
Klíčová slova Orthogonality space; Orthoset; Hilbert space; Normal orthogonality space; Boolean subalgebra
Popis An orthogonality space is a set X together with a symmetric and irreflexive binary relation ?, called the orthogonality relation. A block partition of X is a partition of a maximal set of mutually orthogonal elements of X, and a decomposition of X is a collection of subsets of X each of which is the orthogonal complement of the union of the others. (X, ?) is called normal if any block partition gives rise to a unique decomposition of the space. The set of one-dimensional subspaces of a Hilbert space equipped with the usual orthogonality relation provides the motivating example. Together with the maps that are, in a natural sense, compatible with the formation of decompositions from block partitions, the normal orthogonality spaces form a category, denoted by NOS. The objective of the present paper is to characterise both the objects and the morphisms of NOS from various perspectives as well as to compile basic categorical properties of NOS.
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