On the problem of continuation of unbounded measures on projectors to weights
type: Item
instance of: scholarly article
title: On the problem of continuation of unbounded measures on projectors to weights
zbMATH Open document ID: 0968.46050
author: G. D. Lugovaya
author: Anatoly N. Sherstnev
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: The problem of the noncommutative measure theory consisting of studying the possibility of continuing orthoadditive measures on orthoprojectors of von Neumann algebras to linear functionals is considered. The paper contains a construction of a von Neumann algebra \(M\) with no direct terms of type \(I_2\) and a finitely additive unbounded semifinite measure \(m: M^{pr}\to \{0,+\infty\}\), where \(M^{pr}\) is the set of orthoprojectors in \(M^+\), on \(M\) such that \(m\) cannot be extended to a weight.
reviewed by: Victor Sharapov
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46G12
zbMATH DE Number: 1557644
zbMATH Keywords: weight
zbMATH Keywords: noncommutative measure theory
zbMATH Keywords: continuing orthoadditive measures on orthoprojectors of von Neumann algebras to linear functionals
zbMATH Keywords: additive unbounded semifinite measure
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557644