Czechoslovak Mathematical Journal, first online, pp. 1-11


A note on L-Dunford-Pettis sets in a topological dual Banach space

Abderrahman Retbi

Received March 18, 2019.   Published online April 30, 2020.

Abstract:  The present paper is devoted to some applications of the notion of L-Dunford-Pettis sets to several classes of operators on Banach lattices. More precisely, we establish some characterizations of weak Dunford-Pettis, Dunford-Pettis completely continuous, and weak almost Dunford-Pettis operators. Next, we study the relationships between L-Dunford-Pettis, and Dunford-Pettis (relatively compact) sets in topological dual Banach spaces.
Keywords:  L-Dunford-Pettis set; weak almost Dunford-Pettis operator; weak Dunford-Pettis property; Banach lattice
Classification MSC:  46A40, 46B40, 46B42
DOI:  10.21136/CMJ.2020.0119-19

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Affiliations:   Abderrahman Retbi, Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, Avenue de L'Université, B.P.133, Kénitra, Morocco, e-mail: abderrahmanretbi@hotmail.com


 
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