Characterization of spaces of filtering states
type: Item
instance of: scholarly article
title: Characterization of spaces of filtering states
zbMATH Open document ID: 1241.06006
author: Mirko Navara
published in: International Journal of Theoretical Physics
publication date: 2011-01-12T00:00:00Z
review text: The set of states of an orthomodular lattice (OML) can be empty. If an OML \(L\) admits at least one state, the state space, \(\Omega(L),\) is a convex compact set whose set of \(\sigma\)-additive states forms a face. In the present paper, the author answers the question, which faces correspond to the set of filtering states. The main result is Theorem 2 which says: Let \(C\) be a compact convex sets and \(F\) a semi-exposed face of \(C.\) Then there are an OML \(L\) and an affine homeomorphism \(\phi: C \to \Omega(L)\) such that \(\phi(F) = \Omega_f(L),\) where \(\Omega_f(L)\) is the set of filtering states on \(L.\)
reviewed by: Anatolij Dvurečenskij
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 5835422
zbMATH Keywords: orthomodular lattice
zbMATH Keywords: finitely additive state
zbMATH Keywords: \(\sigma\)-additive state
zbMATH Keywords: filtering state
zbMATH Keywords: semi-exposed face
MaRDI profile type: Publication
full work available at URL: s10773-009-0213-9
OpenAlex ID: W2056316193
cites work: Q3222894
cites work: Yosida-Hewitt and Lebesgue decompositions of states on orthomodular posets
cites work: Q3153698
cites work: Q2762622
cites work: Orthomodular lattices admitting no states
cites work: Q4750696
cites work: Q5427869
cites work: Small quantum structures with small state spaces
cites work: Existence of states on quantum structures
cites work: A characterization of \(\sigma\)-state spaces of orthomodular lattices
cites work: Orthomodular structures as quantum logics. Transl. from the Slovak
cites work: Q4726887
cites work: Q3970639
cites work: Weakly Purely Finitely Additive Measures
cites work: A characterization of state spaces of orthomodular lattices
cites work: Finitely Additive Measures
DOI: 10.1007/S10773-009-0213-9
description: scientific article; zbMATH DE number 5835422