Unbounded absolutely weak Dunford-Pettis operators

Gezer, Niyazi Anıl
Zabeti, Omid
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.


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Citation Formats
N. ERKURŞUN ÖZCAN, N. A. Gezer, and O. Zabeti, “Unbounded absolutely weak Dunford-Pettis operators,” TURKISH JOURNAL OF MATHEMATICS, pp. 2731–2740, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56895.