Banach Lattices with Weak Dunford-Pettis Property

We introduce and study the class of weak almost Dunford-Pettis operators. As an application, we characterize Banach lattices with the weak Dunford-Pettis property. Also, we establish some sufficient conditions for which each weak almost Dunford-Pettis operator is weak Dunford-Pettis. Finally, we derive some interesting results.





References:
[1] Aliprantis C.D. and Burkinshaw O., Dunford-Pettis operators on Banach
lattices. Trans. Amer. Math. Soc. vol. 274, 1 (1982) 227-238.
[2] Aliprantis C. D. and Burkinshaw O., Positive operators. Reprint of the
1985 original. Springer, Dordrecht, 2006.
[3] Bouras, K., Moussa, M. and Aqzzouz, B, Almost Dunford-Pettis sets in
Banach lattices. Preprint.
[4] Kalton N.J. and Saab P., Ideal properties of regular operators between
Banach lattices. Illinois Journal of Math. Vol. 29, 3 (1985) 382-400.
[5] Wnuk W., Banach Lattices with the weak Dunford-Pettis Property, Atti
Sem. Mat. Univ. Modena, XLII, 227-236 (1994).