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Keywords:
weakly compact operator; order continuous norm; KB-space
Summary:
We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we give some consequences.
References:
[1] Aliprantis, Ch. D., Burkinshaw, O.: Positive Operators. Reprint of the 1985 original. Springer, Berlin (2006). MR 2262133 | Zbl 1098.47001
[2] Aqzzouz, B., Nouira, R., Zraoula, L.: About positive Dunford-Pettis operators on Banach lattices. J. Math. Anal. Appl. 324 (2006), 49-59. DOI 10.1016/j.jmaa.2005.10.083 | MR 2262455 | Zbl 1112.47028
[3] Aqzzouz, B., Elbour, A.: On the weak compactness of b-weakly compact operators. Positivity 14 (2010), 75-81. DOI 10.1007/s11117-009-0006-7 | MR 2596465 | Zbl 1198.47034
[4] Aqzzouz, B., Elbour, A., Hmichane, J.: Some properties of the class of positive Dunford-Pettis operators. J. Math. Anal. Appl. 354 (2009), 295-300. DOI 10.1016/j.jmaa.2008.12.063 | MR 2510440 | Zbl 1167.47033
[5] Schaefer, H. H.: Banach Lattices and Positive Operators. Die Grundlehren der mathematischen Wissenschaften 215, Springer-Verlag, Berlin and New York (1974). MR 0423039 | Zbl 0296.47023
[6] Meyer-Nieberg, P.: Banach lattices. Universitext. Springer-Verlag, Berlin (1991). MR 1128093 | Zbl 0743.46015
[7] Wickstead, A. W.: Converses for the Dodds-Fremlin and Kalton-Saab theorems. Math. Proc. Camb. Philos. Soc. 120 (1996), 175-179. DOI 10.1017/S0305004100074752 | MR 1373356 | Zbl 0872.47018
[8] Wnuk, W.: Some characterizations of Banach lattices with the Schur property. Congress on Functional Analysis (Madrid, 1988). Rev. Mat. Univ. Complutense Madr. {\it 2}, No. Suppl., (1989), 217-224. MR 1057221 | Zbl 0717.46018
[9] Zaanen, A. C.: Riesz Spaces II. North-Holland Mathematical Library 30, Amsterdam-New York-Oxford, North-Holland Publishing Company (1983). MR 0704021 | Zbl 0519.46001
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