Some results on disjointly weakly compact sets

AKAY B., GÖK Ö.

Demonstratio Mathematica, cilt.58, sa.1, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 58 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1515/dema-2025-0169
  • Dergi Adı: Demonstratio Mathematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: almost Grothendieck set, Banach lattice, disjointly weakly compact set, order continuous norm, reciprocal Dunford-Pettis set
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.