Weak Compactness of Almost Limited Operators

Weak Compactness of Almost Limited Operators

This paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that if F is a σ-Dedekind complete Banach lattice, then every almost limited operator T:E→F is weakly compact if and only if E is reflexive or the norm of F is order continuous. Also, we...

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Main Authors: Aziz Elbour, Nabil Machrafi, Mohammed Moussa
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2014/263159
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spelling doaj-2463b8ee29bd4850a965a7e70532ed462020-11-25T00:17:39ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/263159263159Weak Compactness of Almost Limited OperatorsAziz Elbour0Nabil Machrafi1Mohammed Moussa2Département de Mathématiques, Faculté des Sciences et Techniques, Université Moulay Ismaïl, BP 509, 52000 Errachidia, MoroccoDépartement de Mathématiques, Faculté des Sciences, Université Ibn Tofail, BP 133, 14000 Kénitra, MoroccoDépartement de Mathématiques, Faculté des Sciences, Université Ibn Tofail, BP 133, 14000 Kénitra, MoroccoThis paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that if F is a σ-Dedekind complete Banach lattice, then every almost limited operator T:E→F is weakly compact if and only if E is reflexive or the norm of F is order continuous. Also, we show that if E is a σ-Dedekind complete Banach lattice, then the square of every positive almost limited operator T:E→E is weakly compact if and only if the norm of E is order continuous.http://dx.doi.org/10.1155/2014/263159
collection DOAJ
language English
format Article
sources DOAJ
author Aziz Elbour
Nabil Machrafi
Mohammed Moussa
spellingShingle Aziz Elbour
Nabil Machrafi
Mohammed Moussa
Weak Compactness of Almost Limited Operators
Journal of Function Spaces
author_facet Aziz Elbour
Nabil Machrafi
Mohammed Moussa
author_sort Aziz Elbour
title Weak Compactness of Almost Limited Operators
title_short Weak Compactness of Almost Limited Operators
title_full Weak Compactness of Almost Limited Operators
title_fullStr Weak Compactness of Almost Limited Operators
title_full_unstemmed Weak Compactness of Almost Limited Operators
title_sort weak compactness of almost limited operators
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2014-01-01
description This paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that if F is a σ-Dedekind complete Banach lattice, then every almost limited operator T:E→F is weakly compact if and only if E is reflexive or the norm of F is order continuous. Also, we show that if E is a σ-Dedekind complete Banach lattice, then the square of every positive almost limited operator T:E→E is weakly compact if and only if the norm of E is order continuous.
url http://dx.doi.org/10.1155/2014/263159
work_keys_str_mv AT azizelbour weakcompactnessofalmostlimitedoperators
AT nabilmachrafi weakcompactnessofalmostlimitedoperators
AT mohammedmoussa weakcompactnessofalmostlimitedoperators
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