Pettis' lemma and topological properties of dual algebras
type: Item
instance of: scholarly article
title: Pettis' lemma and topological properties of dual algebras
zbMATH Open document ID: 0632.47034
published in: Michigan Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: Based on Pettis' lemma, the authors prove the following theorems: Let \({\mathcal A}\) be a weak* closed subspace of L(\({\mathcal H})\) (\({\mathcal H}\) being a complex Hilbert space) where the weak and weak* topologies agree. Then \({\mathcal A}\) has property \((A_{1/n}(r))\) for some n and r. Further, if \({\mathcal A}\) is a weak* closed subspace with property \((A_{1/m})\), then it has the property \((A_{1/2m}(r))\) for some r. Thus, \((A_{1/n})\) means that every [L] in \(Q_{{\mathcal A}}\) can be written as \(\sum^{h}_{i=1}[x_ i\otimes y_ i]\) (sum of operators of rank 1), \((A_{1/n}(r))\) means that this composition also fulfills \[ \sum^{n}_{n=1}\| x_ i\| \| y_ i\| \leq C\| [L]\| \] for any \(C>r\).
Mathematics Subject Classification ID: 47L50
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 4028225
author: Bernard Chevreau
author: Jean Esterle
reviewed by: Alfred Wehrl
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003491
OpenAlex ID: W2091589584
Wikidata QID: Q125054514
DOI: 10.1307/MMJ/1029003491
description: scientific article; zbMATH DE number 4028225