Introduction to the theory of noncommutative integration
type: Item
instance of: scholarly article
title: Introduction to the theory of noncommutative integration
zbMATH Open document ID: 0616.46058
DOI: 10.1007/BF01103856
author: N. V. Trunov
author: Anatoly N. Sherstnev
published in: Journal of Soviet Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The paper is a review of the progress in the theory of noncommutative integration since the well known Segal's work with the emphasis on the works of A. N. Sherstnev and his disciples in Kazan. It contains sections: 1. Integration in von Neumann algebras. 2. On the integration in JBW-algebras. 3. On a problem of integration with respect to unbounded measures on the projections. In the first section various ways to generalize the Segal's theory are described, among them the description of the space \(L_ 1\) with respect to a weight in terms of integrable bilinear forms and constructions of scales of \(L_ p\)-spaces proposed by Sherstnev, Trunov, Haagerup and many others. The second section deals with similar questions in the JBW-setting and is based mainly on Trunov's work. In the third section results of Sherstnev and Lugovaya are formulated.
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 46L70
zbMATH DE Number: 3998539
zbMATH Keywords: noncommutative integration
zbMATH Keywords: Integration in von Neumann algebras
zbMATH Keywords: integration in JBW-algebras
zbMATH Keywords: integration with respect to unbounded measures on the projections
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01103856
OpenAlex ID: W1989809706
description: scientific article; zbMATH DE number 3998539