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.
uaw-Convergence, uaw-Dunford-Pettis operator, Banach lattice
ÖZCAN, NAZİFE ERKURŞUN; GEZER, NİYAZİ ANIL; and ZABETI, OMID
"Unbounded absolutely weak Dunford-Pettis operators,"
Turkish Journal of Mathematics: Vol. 43:
6, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss6/6