Some results on disjointly weakly compact sets
Demonstratio Mathematica, cilt.58, sa.1, 2025 (SCI-Expanded, Scopus)
- 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.