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Almost Dunford–Pettis sets in Banach lattices

Content Provider	Springer Nature Link
Author	Bouras, Khalid
Copyright Year	2013
Abstract	We introduce and study the class of almost Dunford–Pettis sets in Banach lattices. It also discusses some of the consequences derived from this study. As an application, we characterize Banach lattices whose relatively weakly compact sets are almost Dunford–Pettis sets. Also, we establish some necessary and sufficient conditions on which an almost Dunford–Pettis set is L-weakly compact (respectively, relatively weakly compact). In particular, we characterize Banach lattices under which almost Dunford–Pettis sets in the topological dual of a Banach lattice coincide with that of L-weakly compact (respectively, relatively weakly compact) sets. As a consequences we derive some results.
Starting Page	227
Ending Page	236
Page Count	10
File Format	PDF
ISSN	0009725X
Journal	Rendiconti del Circolo Matematico di Palermo
Volume Number	62
Issue Number	2
e-ISSN	19734409
Language	English
Publisher	Springer Milan
Publisher Date	2013-01-25
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Almost Dunford–Pettis set Relatively weakly compact sets L-weakly compact sets Weak Dunford–Pettis property KB-space Positive Schur property Ordered topological linear spaces, vector lattices Ordered normed spaces Banach lattices Mathematics Algebra Geometry Analysis Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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On the class of weak $$^{\star }$$ Dunford–Pettis operators

Some Generalizations on Positive Dunford–Pettis Operators

On the duality problem of positive Dunford-Pettis operators on Banach lattices

Positive almost Dunford–Pettis operators and their duality

On a Question of Bouras concerning weak compactness of almost Dunford-Pettis sets

On the class of positive almost weak Dunford–Pettis operators

On the Product of Almost Dunford–Pettis and Order Weakly Compact Operators

About b-weakly compact operators on Banach lattices

ON A QUESTION OF BOURAS CONCERNING WEAK COMPACTNESS OF ALMOST DUNFORD–PETTIS SETS

Almost Dunford–Pettis sets in Banach lattices

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On the class of weak $$^{\star }$$ Dunford–Pettis operators

Some Generalizations on Positive Dunford–Pettis Operators

On the duality problem of positive Dunford-Pettis operators on Banach lattices

Positive almost Dunford–Pettis operators and their duality

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Almost Dunford–Pettis sets in Banach lattices