Some results on disjointly weakly compact sets

AKAY B., GÖK Ö.

Demonstratio Mathematica, vol.58, no.1, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 58 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1515/dema-2025-0169
  • Journal Name: Demonstratio Mathematica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Keywords: almost Grothendieck set, Banach lattice, disjointly weakly compact set, order continuous norm, reciprocal Dunford-Pettis set
  • Yıldız Technical University Affiliated: Yes

Abstract

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.