Some results on non-commutative Banach function spaces
type: Item
instance of: scholarly article
title: Some results on non-commutative Banach function spaces
zbMATH Open document ID: 0759.46057
DOI: 10.1007/BF02571813
author: Keiichi Watanabe
published in: Mathematische Zeitschrift
publication date: 1993-02-02T00:00:00Z
full work available at URL: https://eudml.org/doc/174418
review text: Let \({\mathcal M}\) be a semifinite von Neumann algebra. We define a system of axioms for non-commutative Banach function spaces as an analogue of that for commutative spaces. We show that, if \({\mathcal M}\) is a \(\sigma\)-finite II\(_ 1\)-factor, then there exists a bijective correspondence between rearrangement invariant function norms on \([0,1]\) and non-commutative Banach function spaces associated with \({\mathcal M}\). Furthermore, the separability of those spaces are characterized in terms of the function norms and the predual of \({\mathcal M}\).
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 46L85
zbMATH DE Number: 108645
zbMATH Keywords: semifinite von Neumann algebra
zbMATH Keywords: non-commutative Banach function spaces
zbMATH Keywords: rearrangement invariant function norms
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 108645