Unbounded absolutely weak Dunford-Pettis operators


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

TURKISH JOURNAL OF MATHEMATICS, cilt.43, ss.2731-2740, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 43 Konu: 6
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3906/mat-1904-27
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.2731-2740

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.