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Semi-compactness of positive Dunford-Pettis operators on Banach lattices
Author(s):
Belmesnaoui
Aqzzouz;
Redouane
Nouira;
Larbi
Zraoula
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1997-2006.
MSC (2000):
Primary 46A40, 46B40, 46B42
Posted:
February 19, 2008
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Abstract:
We investigate Banach lattices on which each positive Dunford-Pettis operator is semi-compact and the converse. As an interesting consequence, we obtain Theorem 2.7 of Aliprantis-Burkinshaw and an element of Theorem 1 of Wickstead.
References:
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- 1.
- Aliprantis, C.D., and Burkinshaw, O., Dunford-Pettis operators on Banach lattices. Trans. Amer. Math. Soc. vol. 274, 1 (1982) 227-238. MR 670929 (84b:47045)
- 2.
- Aliprantis, C.D., and Burkinshaw, O., Locally solid Riesz spaces with applications to economics. Second edition. Mathematical Surveys and Monographs, 105. American Mathematical Society, Providence, RI, 2003. MR 2011364 (2005b:46010)
- 3.
- Aliprantis, C.D., and Burkinshaw, O., Positive operators. Springer-Verlag, Berlin and Heidelberg, 2006. (This monograph was reprinted by Springer-Verlag in 2006.) MR 2262133
- 4.
- Aqzzouz, B., Nouira R., and Zraoula L., Compacité des opérateurs de Dunford-Pettis positifs sur les treillis de Banach. C. R. Math. Acad. Sci. Paris 340, 1 (2005) 37-42. MR 2112038 (2005m:47081)
- 5.
- Aqzzouz, B., Nouira, R., and Zraoula, L., About positive Dunford-Pettis operators on Banach lattices. J. Math. Anal. Appl. 324, 1 (2006) 49-59. MR 2262455
- 6.
- Aqzzouz, B., Nouira, R., and Zraoula, L., Les opérateurs de Dunford-Pettis positifs qui sont faiblement compacts. Proc. Amer. Math. Soc. 134 (2006) 1161-1165. MR 2196052 (2006h:46015)
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Additional Information:
Belmesnaoui
Aqzzouz
Affiliation:
Département d'Economie, Faculté des Sciences Economiques, Juridiques et Sociales, Université Mohammed V-Souissi, B.P. 5295, Sala Eljadida, Morocco
Email:
baqzzouz@hotmail.com
Redouane
Nouira
Affiliation:
Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, B.P. 133, Kénitra, Morocco
Larbi
Zraoula
Affiliation:
Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, B.P. 133, Kénitra, Morocco
DOI:
10.1090/S0002-9939-08-09032-1
PII:
S 0002-9939(08)09032-1
Keywords:
Semi-compact operator,
Dunford--Pettis operator,
order continuous norm,
discrete vector lattice
Received by editor(s):
February 24, 2006
Received by editor(s) in revised form:
December 2, 2006
Posted:
February 19, 2008
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2008,
American Mathematical Society
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