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Keywords:
almost weak$^{\star}$ Dunford-Pettis operator; almost Dunford-Pettis operator; weak Dunford-Pettis$^{\star}$ property; positive Schur property; order continuous norm
almost weak$^{\star}$ Dunford-Pettis operator; almost Dunford-Pettis operator; weak Dunford-Pettis$^{\star}$ property; positive Schur property; order continuous norm
Summary:
In this paper, we introduce and study the class of almost weak$^{\star}$ Dunford-Pettis operators. As consequences, we derive the following interesting results: the domination property of this class of operators and characterizations of the wDP$^{\star}$ property. Next, we characterize pairs of Banach lattices for which each positive almost weak$^{\star}$ Dunford-Pettis operator is almost Dunford-Pettis.
References:
[1] Aliprantis C.D., Burkinshaw O.: Positive Operators. reprint of the 1985 original, Springer, Dordrecht, 2006. MR 2262133 | Zbl 1098.47001
[2] Chen J.X., Chen Z.L., Guo J.X.: Almost limited sets in Banach lattices. J. Math. Anal. Appl 412 (2014), 547–553; doi 10.1016/j.jmaa.2013.10.085. DOI 10.1016/j.jmaa.2013.10.085 | MR 3145821
[3] Dodds P.G., Fremlin D.H.: Compact operators on Banach lattices. Israel J. Math. 34 (1979), 287–320. DOI 10.1007/BF02760610 | MR 0570888
[4] El Kaddouri A., H'michane J., Bouras K., Moussa M.: On the class of weak* Dunford-Pettis operators. Rend. Circ. Mat. Palermo, 62 (2013), 261–265; doi 10.1007/s12215-013-0122-x. DOI 10.1007/s12215-013-0122-x | MR 3090876 | Zbl 1287.46010
[5] Meyer-Nieberg P.: Banach Lattices. Universitext, Springer, Berlin, 1991. MR 1128093 | Zbl 0743.46015
[6] Wnuk W.: Banach Lattices with the weak Dunford-Pettis property. Atti Sem. Mat.Fis. Univ. Modena 42 (1994), no. 1, 227–236. MR 1282338 | Zbl 0805.46023
[7] Wnuk W.: Remarks on J.R. Holub's paper concerning Dunford-Pettis operators. Math. Japon, 38 (1993), 1077–1080. MR 1250331 | Zbl 0799.47020
[8] Wnuk W.: Banach Lattices with Order Continuous Norms. Polish Scientific Publishers, Warsaw, 1999. Zbl 0948.46017
[9] Wnuk W.: Banach lattices with property of the Schur type - a survey. Confer. Sem. Mat. Univ. Bari 249 (1993), no. 25. MR 1230964
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