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Some results on almost L-weakly and almost M-weakly compact operators

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Abstract

The class of weakly compact operators does not contain that of almost L-weakly compact operators. In this paper, we provide a complete answer by giving necessary and sufficient conditions for which every positive almost L-weakly compact operator \(T:E\rightarrow F\) between two Banach lattices is weakly compact. On the other hand, we investigate conditions under which the adjoint operator of every positive almost L-weakly compact operator is almost M-weakly compact.

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References

  1. Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Springer, Berlin (2006)

    Book  Google Scholar 

  2. Afkir, F., Bouras, K., Elbour, A., El Filali, S.: Weak compactness of almost L-weakly and almost M-weakly compact operators. Quaest. Math. 44(9), 1145–1154 (2021). https://doi.org/10.2989/16073606.2020.1777482

    Article  MathSciNet  MATH  Google Scholar 

  3. Bouras, K., Lhaimer, D., Moussa, M.: On the class of almost L-weakly and almost M-weakly compact operators. Positivity 22, 1433–1443 (2018). https://doi.org/10.1007/s11117-018-0586-1

    Article  MathSciNet  MATH  Google Scholar 

  4. Elbour, A., Afkir, F., Sabiri, M.: Some properties of almost L-weakly and almost M-weakly compact operators. Positivity 24, 141–149 (2020). https://doi.org/10.1007/s11117-019-00671-7

    Article  MathSciNet  MATH  Google Scholar 

  5. Aqzzouz, B., Elbour, A., Hmichane, J.: The duality problem for the class of \(b\)-weakly compact operators. Positivity 13, 683–692 (2009). https://doi.org/10.1007/s11117-008-2288-6

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  Google Scholar 

  7. Meyer-Nieberg, P.: Uber Klassen Schwach Kompakter Operatoren in Banachverbanden. Math. Z. 138, 145–159 (1974). https://doi.org/10.1007/BF01214230

    Article  MathSciNet  MATH  Google Scholar 

  8. Wnuk, W.: Banach Lattices with Order Continuous Norms. Polish Scientific Publishers PWN, Warszawa (1999)

    MATH  Google Scholar 

  9. Zaanen, A.C.: Riesz Spaces II. North Holland Publishing Company, Amsterdam (1983)

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Regional Center for Education and Formation (CRMEF), Rabat, Morocco

    Redouane Nouira

  2. Laboratory LMA ENS, Hassan II University of Casablanca, Casablanca, Morocco

    Driss Lhaimer

  3. Department of Mathematics, Faculty of Sciences and Technologies, Moulay Ismail University of Meknes, Boutalamine, P.O. Box 509, 52000, Errachidia, Morocco

    Aziz Elbour

Authors
  1. Redouane Nouira
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  2. Driss Lhaimer
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  3. Aziz Elbour
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Correspondence to Redouane Nouira.

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Nouira, R., Lhaimer, D. & Elbour, A. Some results on almost L-weakly and almost M-weakly compact operators. Positivity 26, 39 (2022). https://doi.org/10.1007/s11117-022-00911-3

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  • DOI: https://doi.org/10.1007/s11117-022-00911-3

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