Preduals of von Neumann algebras
type: Item
instance of: scholarly article
title: Preduals of von Neumann algebras
zbMATH Open document ID: 1053.46039
DOI: 10.1023/A:1024417325676
publication date: 2004-05-18T00:00:00Z
review text: In the paper under review, the author summarizes and sketches the proofs of the results given in the papers [Russ. J. Math. Phys. 10, 117--120 (2003; Zbl 1065.46039)] and [Adv. Stud. Contemp. Math., Kyungshang 7, 1--10 (2003; Zbl 1047.46042)]. The main results of the present paper are the following (from the abstract): (1) If the Banach space of a von Neumann algebra \({\mathcal A}\) is the third dual of some Banach space, then the space \({\mathcal A}\) is isometrically isomorphic to the second dual of some von Neumann algebra \(A\) and the von Neumann algebra \(A\) is uniquely determined by its enveloping von Neumann algebra and is the unique second preduals of \(\mathcal{A}\). (2) An infinite-dimensional von Neumann algebra cannot have preduals of all orders. I strongly recommend to see [Zbl 1047.46042] for an assessment of these results.
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 2065925
zbMATH Keywords: preduals of von Neumann algebras
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: completely positive mapping
zbMATH Keywords: minimal projections
zbMATH Keywords: normal states
author: A. I. Shtern
reviewed by: Miguel Martín
MaRDI profile type: Publication
full work available at URL: a:1024417325676
OpenAlex ID: W2094464908
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 2065925