Nazife ERKURŞUN ÖZCAN, Niyazi Anıl GEZER, Omid ZABETI

Unbounded absolutely weak Dunford–Pettis operators

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

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