Domination by positive Dunford-Pettis completely continuous operators
type: Item
instance of: scholarly article
title: Domination by positive Dunford-Pettis completely continuous operators
zbMATH Open document ID: 1412.46031
author: Kamal El Fahri
author: Mohammed Moussa
published in: Afrika Matematika
publication date: 2018-01-22T00:00:00Z
review text: An operator \(T\) on a Banach space \(X\) is \(DPcc\) if, and only if, for each Dunford-Pettis set \(A\subset X,\) the set \(T(A)\) is relatively compact. We recall that a norm bounded subset \(A\) of \(X\) is a Dunford-Pettis set whenever every weakly compact operator from \(X\) to an arbitrary Banach space carries \(A\) to a norm totally bounded set. The authors consider the domination problem for the class of positive Dunford-Pettis completely continuous operators, abbreviated DPcc. More precisely, they extend a previous paper of \textit{Y.-M. Wen} and \textit{J.-X. Chen} [Adv. Math., Beijing 45, No. 1, 122--132 (2016; Zbl 1374.47031)]. The main results are Theorems 3.6, 3.11 and Corollary 3.7. We state only Theorem 3.6: Let \(E\) and \(F\) be Banach lattices such that the norm of \(F\) is order continuous. If \(T\) is DPcc and \(0\leq S\leq T:E \to F\), then \(S\) is also DPcc.
reviewed by: Nicolae Popa
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 46B50
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 47B07
zbMATH DE Number: 6828496
zbMATH Keywords: Dunford-Pettis completely continuous operator
zbMATH Keywords: order weakly compact operator
zbMATH Keywords: order continuous norm
zbMATH Keywords: Dunford-Pettis set
zbMATH Keywords: Banach lattice
MaRDI profile type: Publication
full work available at URL: s13370-016-0411-6
OpenAlex ID: W2293894139
cites work: Q5665690
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DOI: 10.1007/S13370-016-0411-6
description: scientific article; zbMATH DE number 6828496