Banach-Saks sets in Banach lattices

Authors

  • F. Afkir National School of Applied Sciences of Safi, Cadi Ayyad University, Route Sidi Bouzid, BP 63, Safi 46000, Morocco https://orcid.org/0000-0002-6060-504X
  • M. Hajji Higher Institute of Applied Sciences and Technology of Kasserine, BP 471, 1200 Kasserine, Tunisia
https://doi.org/10.15330/cmp.18.2.478-486

Keywords:

Banach-Saks set, relatively weakly compact set, $L$-weakly compact set, order weakly compact operator, almost Dunford-Pettis operator, Banach lattice
Published online: 2026-10-24

Abstract

We study the Banach-Saks sets in Banach lattices. It also investigated some of the consequences derived from this study. Among other things, we establish that each $L$-weakly compact set is Banach-Saks. Also, we characterize Banach lattices in which the solid hull of a Banach-Saks set is also Banach-Saks. Next, we give a necessary and sufficient condition under which an order bounded almost Dunford-Pettis operator between two Banach lattices maps Banach-Saks sets into $L$-weakly compact sets. In addition, we establish a new characterization of Banach lattices with order continuous norm and order weakly compact operators using Banach-Saks set and the Cesaro convergence.

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How to Cite
(1)
Afkir, F.; Hajji, M. Banach-Saks Sets in Banach Lattices. Carpathian Math. Publ. 2026, 18, 478-486.