Converse of the Eilers-Horst theorem
type: Item
instance of: scholarly article
title: Converse of the Eilers-Horst theorem
zbMATH Open document ID: 0631.46067
DOI: 10.1007/BF00670571
published in: International Journal of Theoretical Physics
publication date: 1987-01-01T00:00:00Z
review text: The theorem of \textit{M. Eilers}, \textit{E. Horst} [Int. J. Theor. Phys. 13, 419-424 (1975; Zbl 0345.46021)] is generalized showing that any finite as well as any \(\sigma\)-finite measure on a quantum logic of a Hilbert space H is a Gleason one iff the dimension of H is a nonmeasurable cardinal \(\neq 2\).
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 46L30
zbMATH DE Number: 4026152
zbMATH Keywords: nonmeasurable cardinal
zbMATH Keywords: Gleason state
zbMATH Keywords: \(\sigma \)-finite measure on a quantum logic
author: Anatolij Dvurečenskij
MaRDI profile type: Publication
cites work: Generalization of Gleason's theorem
cites work: Generalization of Maeda's theorem
cites work: The theorem of Gleason for non-separable Hilbert spaces
cites work: Q3245484
cites work: Q3891824
full work available at URL: https://doi.org/10.1007/bf00670571
OpenAlex ID: W1965004459
description: scientific article; zbMATH DE number 4026152