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On the domination of limited and order Dunford-Pettis operators

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Abstract

We study the domination problem for the class of limited operators and that of order limited operators. On the other hand, we show that the class of order Dunford–Pettis operators satisfies the domination problem.

Résumé

Nous étudions le problème de domination pour la classe des opérateurs limités et celle des opérateurs limités pour l’ordre. D’autre part, nous montrons que la classe des opérateurs de Dunford-Pettis pour l’ordre satisfait le problème de domination.

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References

  1. Aliprantis, C.D., Burkinshaw, O.: Dunford–Pettis operators on Banach lattices. Trans. Am. Math. Soc. 274(1), 227–238 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Reprint of the 1985 Original. Springer, Dordrecht (2006)

    MATH  Google Scholar 

  3. Andrews, K.T.: Dunford–Pettis sets in the space of Bochner integrable functions. Math. Ann. 241, 35–41 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  4. Aqzzouz, B., Bouras, K.: Dunford–Pettis sets in Banach lattices. Acta Math. Univ. Comen. New Ser. 81, 185–196 (2012)

    MATH  MathSciNet  Google Scholar 

  5. Aqzzouz, B., Nouira, R., Zraoula, L.: Compactness properties for dominated by AM-compact operators. Proc. Am. Math. Soc. 135, 1151–1157 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bourgain, J., Diestel, J.: Limited operators and strict cosingularity. Math. Nachrichten 119, 55–58 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dodds, P.G., Fremlin, D.H.: Compact operators on Banach lattices. Israel J. Math. 34, 287–320 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  8. El Kaddouri, A., Moussa, M.: About the class of ordered limited operators. Acta Univ. Carolinae-Math. Physica 54(1), 37–43 (2013)

  9. Flores, J., Hernández, F.L., Tradacete, P.: Domination problems for strictly singular operators and other related classes. Positivity 15(4), 595–616 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kalton, N.J., Saab, P.: Ideal properties of regular operators between Banach lattices. Ill. J. Math. 29(3), 382–400 (1985)

    MATH  MathSciNet  Google Scholar 

  11. Meyer-Nieberg, P.: Banach Lattices. Universitext, Springer, Berlin (1991)

    Book  MATH  Google Scholar 

  12. Wickstead, A.W.: Converses for the Dodds–Fremlin and Kalton–Saab theorems. Math. Proc. Camb. Philos. Soc. 120, 175–179 (1996)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

The authors would like to thank the referee for his useful comments and suggestions to improve the quality of the paper.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences, Université Moulay Ismail, B.P. 11201, Zitoune, Meknes, Morocco

    J. H’Michane

  2. Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, B.P. 133, Kenitra, Morocco

    K. El Fahri

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  1. J. H’Michane
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  2. K. El Fahri
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Correspondence to J. H’Michane.

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H’Michane, J., El Fahri, K. On the domination of limited and order Dunford-Pettis operators. Ann. Math. Québec 39, 169–176 (2015). https://doi.org/10.1007/s40316-015-0036-4

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  • DOI: https://doi.org/10.1007/s40316-015-0036-4

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