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Weak and almost Grothendieck operators in Banach lattices

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Abstract

In this paper, we introduce and study a weak version of Grothendieck operators that we will call weak Grothendieck operators, these are operators between Banach spaces which exactly carry Dunford–Pettis sets into limited ones. We establish some characterizations of this class of operators. After that, we look for some conditions on the starting space under which this class of operators and that of Grothendieck operators coincide. Furthermore, we study the weak compactness of almost Grothendieck operators. Besides, we present some results concerning the domination property of positive Grothendieck operators. Finally, some connections between almost Grothendieck operators and those whose adjoint carries positive weak* null sequences into weakly null ones are obtained.

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Authors and Affiliations

  1. Faculté des Sciences, Département de Mathématiques, Université Ibn Tofail, B.P. 133, 14000, Kenitra, Morocco

    Fatima Zahra Oughajji

  2. Faculté des sciences, Université Ibn-Tofail, Kenitra, Morocco

    Ilham Essadki & Bouazza El Wahbi

  3. Department of Mathematics, Faculty of Sciences, Ibn Zohr University, Agadir, Morocco

    Kamal El Fahri

  4. Centre Régional des Métiers de l’Éducation et de la Formation-Kenitra, Kenitra, Morocco

    Larbi Zraoula

Authors
  1. Fatima Zahra Oughajji
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  2. Ilham Essadki
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  3. Kamal El Fahri
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  4. Larbi Zraoula
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  5. Bouazza El Wahbi
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Correspondence to Fatima Zahra Oughajji.

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Oughajji, F.Z., Essadki, I., El Fahri, K. et al. Weak and almost Grothendieck operators in Banach lattices. Rend. Circ. Mat. Palermo, II. Ser (2024). https://doi.org/10.1007/s12215-024-01045-z

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  • DOI: https://doi.org/10.1007/s12215-024-01045-z

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