Academic Journal
On the class of order Dunford-Pettis operators
| العنوان: | On the class of order Dunford-Pettis operators |
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| المؤلفون: | Bouras, Khalid, El Kaddouri, Abdelmonaim, H'michane, Jawad, Moussa, Mohammed |
| بيانات النشر: | Institute of Mathematics, Academy of Sciences of the Czech Republic Matematický ústav AV ČR |
| سنة النشر: | 2013 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:Dunford-Pettis operator, keyword:weak Dunford-Pettis operator, keyword:order Dunford-Pettis operator, keyword:order continuous norm, keyword:Schur property, msc:46B40, msc:46B42, msc:47B60 |
| الوصف: | summary:We characterize Banach lattices $E$ and $F$ on which the adjoint of each operator from $E$ into $F$ which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if $E$ and $F$ are two Banach lattices then each order Dunford-Pettis and weak Dunford-Pettis operator $T$ from $E$ into $F$ has an adjoint Dunford-Pettis operator $T'$ from $F'$ into $E'$ if, and only if, the norm of $E'$ is order continuous or $F'$ has the Schur property. As a consequence we show that, if $E$ and $F$ are two Banach lattices such that $E$ or $F$ has the Dunford-Pettis property, then each order Dunford-Pettis operator $T$ from $E$ into $F$ has an adjoint $T'\colon F'\longrightarrow E'$ which is Dunford-Pettis if, and only if, the norm of $E'$ is order continuous or $F'$ has the Schur property. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0862-7959 2464-7136 |
| Relation: | mr:MR3136498; zbl:Zbl 06260034; reference:[1] Aliprantis, C. D., Burkinshaw, O.: Positive Operators. Reprint of the 1985 original.Springer, Berlin (2006). Zbl 1098.47001, MR 2262133; reference:[2] Andrews, K. T.: Dunford-Pettis sets in the space of Bochner integrable functions.Math. Ann. 241 (1979), 35-41. Zbl 0398.46025, MR 0531148, 10.1007/BF01406706; reference:[3] Aqzzouz, B., Bouras, K.: Weak and almost Dunford-Pettis operators on Banach lattices.Demonstr. Math. 46 165-179 (2013). MR 3075506; reference:[4] Aqzzouz, B., Bouras, K.: Dunford-Pettis sets in Banach lattices.Acta Math. Univ. Comen., New Ser. 81 185-196 (2012). MR 2975284; reference:[5] Aqzzouz, B., Bouras, K., Moussa, M.: Duality property for positive weak Dunford-Pettis operators.Int. J. Math. Math. Sci. 2011, Article ID 609287 12 p (2011). Zbl 1262.47057, MR 2821970; reference:[6] Dodds, P. G., Fremlin, D. H.: Compact operators on Banach lattices.Isr. J. Math. 34 (1979), 287-320. MR 0570888, 10.1007/BF02760610; reference:[7] Meyer-Nieberg, P.: Banach Lattices.Universitext. Springer, Berlin (1991). Zbl 0743.46015, MR 1128093 |
| الاتاحة: | http://hdl.handle.net/10338.dmlcz/143438 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.E7D93613 |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 08627959 24647136 |
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