On the weak Dunford-Pettis property
type: Item
instance of: scholarly article
title: On the weak Dunford-Pettis property
zbMATH Open document ID: 0641.46005
DOI: 10.1007/BF01194411
author: Denny H. Leung
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: A Banach space E has the Dunford-Pettis property if every weakly compact operator from E into any Banach space is a Dunford-Pettis operator, i.e., maps weakly compact sets onto norm compact sets. A Banach lattice E has the weak Dunford-Pettis property if every weakly compact operator from E into any Banach space maps disjoint, weakly null sequences onto norm null sequences. We provide an example which serves to distinguish these two properties.
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 4044456
zbMATH Keywords: Dunford-Pettis property
zbMATH Keywords: weakly compact operator
zbMATH Keywords: Dunford-Pettis operator
zbMATH Keywords: weak Dunford-Pettis property
MaRDI profile type: Publication
cites work: Q4188284
cites work: Orlicz spaces and modular spaces
description: scientific article; zbMATH DE number 4044456