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On the class of weak U-Dunford–Pettis operators

Part of: Normed linear spaces and Banach spaces; Banach lattices Special classes of linear operators

Published online by Cambridge University Press:  12 November 2025

Adil Driouich ,
Larbi Zraoula  and
Bouazza El Wahbi
Adil Driouich*
Affiliation:
Faculty of Sciences, University of Ibn Tofail , Kenitra, Morocco e-mail: bouazza.elwahbi@uit.ac.ma
Larbi Zraoula
Affiliation:
Mathematics Department at the Regional Center for the Professions of Education and Training (CRMEF), Kenitra, Morocco e-mail: zraoularbi@yahoo.fr
Bouazza El Wahbi
Affiliation:
Faculty of Sciences, University of Ibn Tofail , Kenitra, Morocco e-mail: bouazza.elwahbi@uit.ac.ma
*
e-mail: adil.driouich@uit.ac.ma
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Abstract

In this article, we define a new class of operators called weak U-Dunford–Pettis, which generalizes the U-Dunford–Pettis, weak Dunford–Pettis, and order Dunford–Pettis classes, then we also give a characterization for this class, which we compare with some lattice properties, we then set out the conditions under which this class coincides with the U-Dunford–Pettis class, the weak Dunford–Pettis class, and the order Dunford–Pettis class.

Keywords

U-Dunford–Pettis propertyweak U-Dunford–Pettis operatorU-Dunford–Pettis operatorweak Dunford–Pettis operatororder Dunford–Pettis operators

MSC classification

Primary: 46B42: Banach lattices 47B60: Operators on ordered spaces 47B65: Positive operators and order-bounded operators 47B07: Operators defined by compactness properties

Information

Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 13
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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References

Aboutafail, O., El Fahri, K., H’Michane, J., and Zraoula, L., On the class of U-Dunford-Pettis operators . Quaest. Math. 45(2022), no. 7, 1041–1055.Google Scholar
Aliprantis, C. D. and Burkinshaw, O., Dunford–Pettis operators on Banach lattices . Trans. Amer. Math. Soc. 274(1982), no. 1, 227–238.Google Scholar
Aliprantis, C. D. and Burkinshaw, O., Positive operators, Reprint of the 1985 original, Springer, Dordrecht, 2006. ISBN: 978-1-4020-6935-8.Google Scholar
Andrews, K., Dunford-Pettis sets in the space of Bochner integrable functions . Math. Ann. 241(1979), no. 1, 35–41.Google Scholar
Aqzzouz, B. and Bourass, K., Dunford-Pettis sets in Banach lattices . Acta Math. Sci. Ser. B (Engl. Ed.) 32(2012), no. 5, 1819–1828.Google Scholar
Aqzzouz, B. and Bourass, K., Weak and almost Dunford-Pettis operators on Banach lattices . Demonstratio Mathematica 46(2013), no. 3, 531–548.Google Scholar
Aqzzouz, B., Bourass, K., and Moussa, M., Duality property for positive weak Dunford-Pettis operators . Int. J. Math. Math. Sci. (2011), Art. ID 383685, 8 pp.Google Scholar
Aqzzouz, B. and Elbour, A., Some results on discrete Banach lattices . Creative Math. Inf. 19(2010), no. 2, 110–111.Google Scholar
Bourass, K., El Kaddouri, M., H’Michane, J., and Moussa, M., On the class of order Dunford-Pettis operators . Math. Bohem. 138(2013), no. 4, 403–415.Google Scholar
Elbour, A. and Aqzzouz, B., Some results on discrete Banach lattices . Creative Math. Inform. 19(2010), no. 2, 110–111.Google Scholar
Meyer-Nieberg, P., Banach lattices. Springer-Verlag, Berlin, 1991.Google Scholar
Zraoula, L., Ouba, I., H’michane, J., and El Wahbi, B., On the class of unbounded-U-Dunford-Pettis operators . Filomat 38(2024), no. 25, 8701–8713. https://doi.org/10.2298/FIL2425701ZGoogle Scholar