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Article

Aqzzouz, Belmesnaoui ; Elbour, Aziz ; Aboutafail, Othman
The weak compactness of almost Dunford-Pettis operators. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 52 (2011), issue 1, pp. 31-35
MSC: 46A40, 46B40, 46B42 | MR 2828372 | Zbl 1240.46040
Keywords:
almost Dunford-Pettis operator; weakly compact operator; order continuous norm; reflexive Banach space
Summary:
We characterize Banach lattices on which every positive almost Dunford-Pettis operator is weakly compact.
References:
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[3] Meyer-Nieberg P.: Banach Lattices. Universitext, Springer, Berlin, 1991. MR 1128093 | Zbl 0743.46015
[4] 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
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