Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
Banach Lattices with Weak Dunford-Pettis Property

Authors: Khalid Bouras, Mohammed Moussa

Abstract:

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.

Keywords: Almost Dunford-Pettis operator, weak Dunford-Pettis operator, eak almost Dunford-Pettis operator, almost Dunford-Pettis operator, weak Dunford-Pettis operator

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062756

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1561

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).