Research Article

A note on the U-Dunford-Pettis operators

Published in: Quaestiones Mathematicae
Volume 48 , issue 3 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 429–436
DOI: 10.2989/16073606.2024.2397564
Author(s): Farid Afkir Moulay Ismail University of Meknes, Morocco, Aziz Elbour Moulay Ismail University of Meknes, Morocco,
Keywords: Primary: 46B42, Secondary: 47B60, 47B65, Dunford-Pettis operator, U-Dunford-Pettis operator, AM-compact operator, order continuous norm, Banach lattice,
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Abstract

The purpose of this note is to give a correct proof of the theorem that concerns the domination property of the class of U-Dunford-Pettis operators obtained by O. Aboutafail, K. El Fahri, J. H’Michane and L. Zraoula [On the class of U-Dunford-Pettis operators, Quaestiones Mathematicae 45(4) (2022), 655–666]. Also, we investigate necessary and sufficient conditions under which U-Dunford–Pettis operators between Banach lattices must be Dunford–Pettis.
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