Generalization of Maeda's theorem
type: Item
instance of: scholarly article
title: Generalization of Maeda's theorem
zbMATH Open document ID: 0618.46053
DOI: 10.1007/BF00671687
author: Anatolij Dvurečenskij
published in: International Journal of Theoretical Physics
publication date: 1986-01-01T00:00:00Z
review text: The theorem of S. Maeda concerning the characterization of finite measures on a quantum logic of all closed subspaces of a Hilbert space of dimension \(\neq 2\) is generalized to the case of \(\sigma\)-finite measures with possible infinite values showing that the following assertions are equivalent: (i) there is unique positive bilinear form \(t\) with a dense domain such that \(m(M)=tr t\circ P^ M\) if \(t\circ P^ M\in Tr(H)\) and \(m(M)=\infty\) otherwise; (ii) \(m\) is totally additive; (iii) \(m\) has a support.
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 4002833
zbMATH Keywords: support
zbMATH Keywords: characterization of finite measures on a quantum logic of all closed subspaces of a Hilbert space of dimension \(\neq 2\)
zbMATH Keywords: \(\sigma \)- finite measures with possible infinite values
zbMATH Keywords: unique
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00671687
OpenAlex ID: W2005301261
description: scientific article; zbMATH DE number 4002833