Order derivations on \(L^ p\)-spaces of \(W^ *\)-algebras
type: Item
instance of: scholarly article
title: Order derivations on \(L^ p\)-spaces of \(W^ *\)-algebras
zbMATH Open document ID: 0615.46061
DOI: 10.1007/BF01179272
author: Lothar M. Schmitt
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173868
review text: An order derivation is by definition a bounded generator of a one- parameter group of positive operators on an ordered Banach space. In this paper we characterize order derivations on \(L^ p\)-spaces of \(W^ *\)- algebras. In fact we show how order derivations are obtained from the standard representation of the \(W^ *\)-algebra on its \(L^ p\)-space. This makes \textit{A. Connes}'s theory of order derivations on Hilbert spaces in standard forms of \(W^ *\)-algebras applicable to the \(L^ p\) spaces [Ann. Inst. Fourier 24(1974), No.4, 121-155 (1975; Zbl 0287.46078)].
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 3996425
zbMATH Keywords: bounded generator of a one-parameter group of positive operators on an ordered Banach space
zbMATH Keywords: order derivations on \(L^ p\)-spaces of \(W^ *\)- algebras
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3996425