Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
Banach lattice; weak almost Dunford-Pettis operator; weak Dunford-Pettis property
Banach lattice; weak almost Dunford-Pettis operator; weak Dunford-Pettis property
Summary:
In this paper, we give some necessary and sufficient conditions such that each positive operator between two Banach lattices is weak almost Dunford-Pettis, and we derive some interesting results about the weak Dunford-Pettis property in Banach lattices.
References:
[1] Aliprantis, C.D., Burkinshaw, O.: Positive operators. Springer, Dordrecht, 2006, Reprint of the 1985 original. MR 2262133
[2] Bouras, K.: Almost Dunford-Pettis sets in Banach lattices. Rend. Circ. Mat. Palermo (2) 62 (2013), 227–236. DOI 10.1007/s12215-013-0105-y | MR 3090872
[3] Bouras, K., Moussa, M.: Banach lattice with weak Dunford-Pettis property. International Journal of Information and Mathematical Sciences 6 (3) (2010), 203–207.
[4] Meyer-Nieberg, P.: Banach lattices. Tech. report, Universitext, 1991, Springer-Verlag, Berlin. MR 1128093 | Zbl 0743.46015
[5] Schaefer, H.H.: Banach Lattices and Positive Operators. Springer-Verlag, Berlin – New York, 1974. MR 0423039 | Zbl 0296.47023
[6] Wnuk, W.: Banach lattices with the weak Dunford-Pettis property. Atti Sem. Mat. Fis. Univ. Modena 42 (1) (1994), 227–236. MR 1282338
[7] Wnuk, W.: Banach Lattices with Order Continuous Norms. Polish Scientific Publishers, Warsaw, 1999.
Search
Partner of
