Unbounded absolutely weak Dunford-Pettis operators

ERKURŞUN ÖZCAN N., Gezer N. A., Zabeti O.

Turkish Journal of Mathematics, cilt.43, sa.6, ss.2731-2740, 2019 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 6
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3906/mat-1904-27
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2731-2740
  • Anahtar Kelimeler: uaw-Convergence, uaw-Dunford-Pettis operator, Banach lattice
  • TED Üniversitesi Adresli: Hayır

Özet

In the present article, we expose various properties of unbounded absolutely weak Dunford-Pettis and unbounded absolutely weak compact operators on a Banach lattice E. In addition to their topological and lattice properties, we investigate relationships between M-weakly compact operators, L-weakly compact operators, and order weakly compact operators with unbounded absolutely weak Dunford-Pettis operators. We show that the square of any positive uaw-Dunford-Pettis (M-weakly compact) operator on an order continuous Banach lattice is compact. Many examples are given to illustrate the essential conditions.