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

Part of: Normed linear spaces and Banach spaces; Banach lattices Topological linear spaces and related structures

Published online by Cambridge University Press:  02 April 2015

JIN XI CHEN  and
LEI LI
JIN XI CHEN*
Affiliation:
Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, PR China email [email protected]
LEI LI
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China email [email protected]
*
✉[email protected]
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Abstract

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We give a positive answer to the question of Bouras [‘Almost Dunford–Pettis sets in Banach lattices’, Rend. Circ. Mat. Palermo (2) 62 (2013), 227–236] concerning weak compactness of almost Dunford–Pettis sets in Banach lattices. That is, every almost Dunford–Pettis set in a Banach lattice $E$ is relatively weakly compact if and only if $E$ is a $\mathit{KB}$-space.

Keywords

almost Dunford–Pettis setL-weakly compact setthe positive Schur propertyKB-spaceBanach lattice

MSC classification

Primary: 46B42: Banach lattices
Secondary: 46A40: Ordered topological linear spaces, vector lattices 46B50: Compactness in Banach (or normed) spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 1 , August 2015 , pp. 111 - 114
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Aliprantis, C. D. and Burkinshaw, O., Positive Operators (reprint of the 1985 original) (Springer, Dordrecht, 2006).Google Scholar
Bouras, K., ‘Almost Dunford–Pettis sets in Banach lattices’, Rend. Circ. Mat. Palermo (2) 62 (2013), 227–236.CrossRefGoogle Scholar
Chen, J. X., Chen, Z. L. and Ji, G. X., ‘Almost limited sets in Banach lattices’, J. Math. Anal. Appl. 412 (2014), 547–553.CrossRefGoogle Scholar
Meyer-Nieberg, P., Banach Lattices (Universitext) (Springer, Berlin, 1991).CrossRefGoogle Scholar
Wnuk, W., ‘Banach lattices with the weak Dunford–Pettis property’, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 42 (1994), 227–236.Google Scholar