About positive weak Dunford–Pettis operators on Banach lattices

We characterize Banach lattices for which each positive weak Dunford–Pettis operator from a Banach lattice into another dual Banach lattice is almost Dunford–Pettis. Also, we give some sufficient and necessary conditions for which the class of positive weak Dunford–Pettis operators coincides with th...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2011-09, Vol.381 (2), p.891-896
Main Authors: Moussa, M., Bouras, K.
Format: Article
Language:English
Subjects:
Dunford–Pettis operator
Exact sciences and technology
Functional analysis
KB-space
Mathematical analysis
Mathematics
Operator theory
Order continuous norm
Positive Schur property
Schur property
Sciences and techniques of general use
Weak Dunford–Pettis operator
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Summary:We characterize Banach lattices for which each positive weak Dunford–Pettis operator from a Banach lattice into another dual Banach lattice is almost Dunford–Pettis. Also, we give some sufficient and necessary conditions for which the class of positive weak Dunford–Pettis operators coincides with that of positive Dunford–Pettis operators, and we derive some consequences.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.04.011