The von Neumann algebra characterization theorems
type: Item
instance of: scholarly article
title: The von Neumann algebra characterization theorems
zbMATH Open document ID: 0576.46043
author: Richard V. Kadison
published in: Expositiones Mathematicae
publication date: 1985-01-01T00:00:00Z
review text: There are two standard characterization theorems that give necessary and sufficient conditions for a \(C^*\)-algebra to be isomorphic to a von Neumann algebra. Sakai's states that these \(C^*\)-algebras are precisely those that are (isometric to) the norm-dual space of some Banach space. The author's states that these \(C^*\)-algebras are the ones that are monotone closed and possess a separating family of normal states. In this paper, the author derives the first characterization from the second. Complete, streamlined proofs are given.
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 3921283
zbMATH Keywords: necessary and sufficient conditions for a \(C^*\)-algebra to be
zbMATH Keywords: isomorphic to a von Neumann algebra
zbMATH Keywords: monotone closed
zbMATH Keywords: separating family of normal states
zbMATH Keywords: necessary and sufficient conditions for a \(C^*\)- algebra to be isomorphic to a von Neumann algebra
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3921283