A note on Jauch-Piron states
type: Item
instance of: scholarly article
title: A note on Jauch-Piron states
zbMATH Open document ID: 0625.03042
DOI: 10.1016/0034-4877(86)90017-0
author: Pavel Pták
published in: Reports on Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: A logic (orthomodular poset) L is called Jauch-Piron if for each state (finitely additive probability measure) s on L and each a, \(b\in L\) the equality \(s(a)=s(b)-1\) implies the existence of \(c\in L\) such that \(c\leq a\), \(c\leq b\), \(s(c)=1\). The author investigates the size of the class of Jauch-Piron logics. Besides general logics he studies these questions for hilbertian and set-representable \((=concrete)\) logics. He compares his results with those obtained for \(\sigma\)-additive states by \textit{L. Bunce}, \textit{M. Navara}, \textit{P. Pták} and \textit{J. D. M. Wright} [Quart. J. Math., Oxford II. Ser. 36, 261-271 (1985; Zbl 0585.03038)].
reviewed by: Mirko Navara
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 4014712
zbMATH Keywords: orthomodular poset
zbMATH Keywords: Jauch-Piron logics
MaRDI profile type: Publication
full work available at URL: 0034-4877(86)90017-0
OpenAlex ID: W2038155628
cites work: QUANTUM LOGICS WITH JAUCH–PIRON STATES
cites work: Q4150220
cites work: Orthomodular lattices admitting no states
cites work: Splittings and iterative methods for approximate solutions to singular operator equations in Hilbert spaces
cites work: Uniqueness and existence properties of bounded observables
cites work: Q5551052
cites work: Q3791155
cites work: Q5516132
cites work: Exotic logics
cites work: Q3712337
cites work: Jauch–Piron states
cites work: A characterization of state spaces of orthomodular lattices
cites work: Q5537293
description: scientific article; zbMATH DE number 4014712