The class of almost order limited operators on Banach latices
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Abstract
We introduce and study the class of almost order limited operators and we derive the following interesting consequence:the domination property of this class of operators, a characteri-zation of the property (d). After that, We characterize Banachlattices E and F on which each operator from E into F whichis almost order limited and weak almost limited is almost limitedoperator.
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H'michane, J.
(2015).
The class of almost order limited operators on Banach latices.
Acta Mathematica Universitatis Comenianae, 84(1), 97-102.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/63/129
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References
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[2] J. Bourgain and J. Diestel, Limited operators and strict cosingularity, Math. Nachr. 119 (1984), 55-58.
[3] Chen J.X., Chen Z.L., Ji G.X.: Almost limited sets in Banach lattices, J. Math. Anal. Appl. 412 (2014) 547-553.
[4] Dodds, P.G. and Fremlin, D.H., Compact operators on Banach lattices, Israel J. Math. 34 (1979), 287-320.
[5] Elbour, A., Machra, N., Moussa, M., On the class of weak almost limited operators. http://arxiv.org/abs/1403.3348.
[6] A. EL Kaddouri, and M. Moussa, About the class of order limited operator. Acta Universitatis Carolinae. vol. 54(2013), no. 1. pp. 37-42.
[7] Machra N., Elbour A., Moussa M.: Some characterizations of almost limited sets and applications. http://arxiv.org/abs/1312.2770.
[8] Meyer-Nieberg, P., Banach lattices, Universitext. Springer-Verlag, Berlin, 1991.
[9] Wnuk W. On the dual positive Schur property in Banach lattices. Positivity (2013) 17:759-773.