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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/263159 |
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| _version_ | 1832562249160458240 |
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| author | Aziz Elbour Nabil Machrafi Mohammed Moussa |
| author_facet | Aziz Elbour Nabil Machrafi Mohammed Moussa |
| author_sort | Aziz Elbour |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-2463b8ee29bd4850a965a7e70532ed46 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-2463b8ee29bd4850a965a7e70532ed462025-02-03T01:23:05ZengWileyJournal 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 |
| spellingShingle | Aziz Elbour Nabil Machrafi Mohammed Moussa Weak Compactness of Almost Limited Operators Journal of Function Spaces |
| title | 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_short | Weak Compactness of Almost Limited Operators |
| title_sort | weak compactness of almost limited operators |
| url | http://dx.doi.org/10.1155/2014/263159 |
| work_keys_str_mv | AT azizelbour weakcompactnessofalmostlimitedoperators AT nabilmachrafi weakcompactnessofalmostlimitedoperators AT mohammedmoussa weakcompactnessofalmostlimitedoperators |