The Radon-Nikodym theorem for \(L^p\)-spaces of \(W^*\)-algebras
type: Item
instance of: scholarly article
title: The Radon-Nikodym theorem for \(L^p\)-spaces of \(W^*\)-algebras
zbMATH Open document ID: 0646.46059
author: Lothar M. Schmitt
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: Summary: We prove an analogue of \textit{S. Sakai}'s [Bull. Am. Math. Soc. 71, 149--151 (1965; Zbl 0132.10803)] Radon-Nikodym theorem for \(L^p\)-spaces of \(W^*\)-algebras. Following \textit{N. Takesaki} [Tomita's theory of modular Hilbert algebras and its application. Berlin etc.: Springer-Verlag (1970; Zbl 0193.42502)] we characterize the Radon-Nikodym derivatives by analytic extensions of modular automorphism groups. Finally, we relate the facial structure in \(L^p\)-spaces of \(W^*\)-algebras to \textit{A. Connes}' [Ann. Ec. Norm. Sup. 6, 133--252 (1973; Zbl 0274.46050)] unitary Radon-Nikodym cocycles.
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
zbMATH DE Number: 4054344
zbMATH Keywords: Radon-Nikodym theorem for \(L^p\)-spaces of \(W^*\)-algebras
zbMATH Keywords: analytic extensions of modular automorphism groups
zbMATH Keywords: facial structure
zbMATH Keywords: unitary Radon-Nikodym cocycles
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195177060
OpenAlex ID: W2072018962
DOI: 10.2977/PRIMS/1195177060
description: scientific article; zbMATH DE number 4054344