Banach-Saks sets in Banach lattices

Source 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.