Some results on disjointly weakly compact sets - Akay, Baris; Gok, Omer (DE GRUYTER POLAND SP Z O O, 2025)
We give an operator characterization of disjointly weakly compact sets and show that disjointly weakly compact sets coincide with reciprocal Dunford-Pettis sets. We compare disjointly weakly compact sets with almost Grothendieck sets, relatively compact sets, and weak reciprocal Dunford-Pettis sets. Consequently, we obtain new characterizations of the weak Grothendieck property, Schur property, and Banach lattices whose dual have an order continuous norm.
Keywords: disjointly weakly compact set; reciprocal Dunford-Pettis set; almost Grothendieck set; Banach lattice; order continuous norm; DUNFORD-PETTIS OPERATORS; LIMITED SETS; Mathematics