Abstract
In this paper, we give some results on the product of positive almost Dunford–Pettis and interval preserving order weakly compact operators. As consequence, we derive some interesting consequences. Also, we look at the dual counterpart.
Similar content being viewed by others
References
Aliprantis, C.D., Burkinshaw, O.: Positive operators, Reprint of the 1985 original. Springer, Dordrecht (2006)
Andrews, K.T.: Dunford-Pettis sets in the space of Bochner integrable functions. Math. Ann. 241, 35–41 (1979)
Aqzzouz, B., Nouira, R., Zraoula, L.: Compactness properties of operators dominated by AM-compact operators. Proc. Am. Math. Soc. 135, 1151–1157 (2007)
Aqzzouz, B., Elbour, A.: Some characterizations of almost Dunford-Pettis operators and applications. Positivity 15(3), 369–380 (2011)
Aqzzouz, B., Elbour, A., Wickstead, A.W.: Positive almost Dunford–Pettis operators and their duality. Positivity 15, 185–197 (2011)
Aqzzouz, B., Bourass, K.: Weak and almost Dunford–Pettis operators on Banach lattices. Demonstr. Math. 46, 165–179 (2013)
Aqzzouz, B., Aboutafail, O., Hmichane, J.: Compactness of b-weakly compact operators. Acta Sci. Math. (Szeged) 78, 163–171 (2012)
Chen, Z.L., Wickstead, A.W.: L-weakly and M-weakly compact operators. Indag. Math. (N.S.) 10(3), 321–336 (1999)
Dodds, P.G., Fremlin, D.H.: Compact operators on Banach lattices. Isr. J. Math. 34, 287–320 (1979)
El Kaddouri, A., Moussa, M.: About the class of ordered limited operators, Acta Universitatis Carolinae. Math. Phys. 54(1), 37–43 (2013)
Machrafi, N., Elbour, A., Moussa, M.: Some characterizations of almost limited sets and applications. arXiv:1312.2770
Meyer-Nieberg, P.: Banach lattices, Universitext. Springer-Verlag, Berlin (1991)
Sanchez, J.A.: Operators on Banach lattices (Spanish), Ph. D. Thesis, Complutense University, Madrid (1985)
Wnuk, W.: Banach lattices with properties of the Schur typea survey. Conf. Sem. Mat. Univ. Bari 249, 1–25 (1993)
Wnuk, W.: Banach lattices with the weak Dunford-Pettis property. Atti Sem. Mat. Fis. Univ. Modena 42(1), 227–236 (1994)
Wnuk, W.: On the dual positive Schur property in Banach lattices. Positivity 17, 759–773 (2013)
Wickstead, A.W.: Converses for the Dodds-Fremlin and Kalton-Saab theorems. Math. Proc. Camb. Philos. Soc. 120, 175–179 (1996)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Henk de Snoo.
Rights and permissions
About this article
Cite this article
El Fahri, K., H’michane, J. On the Product of Almost Dunford–Pettis and Order Weakly Compact Operators. Complex Anal. Oper. Theory 10, 605–615 (2016). https://doi.org/10.1007/s11785-015-0506-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11785-015-0506-3
Keywords
- Almost Dunford–Pettis operator
- Order weakly compact operator
- Almost limited operator
- L-weakly compact set
- Banach lattice