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Title: Some characterizations of order weakly compact operator (English)
Author: Aqzzouz, Belmesnaoui
Author: Elbour, Aziz
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 136
Issue: 1
Year: 2011
Pages: 105-112
Summary lang: English
Category: math
Summary: We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences. (English)
Keyword: order weakly compact operator
Keyword: order continuous norm
Keyword: discrete Banach lattice
Keyword: weakly sequentially continuous lattice operations
MSC: 46A40
MSC: 46B40
MSC: 46B42
MSC: 47B07
MSC: 47B60
idZBL: Zbl 1224.46035
idMR: MR2807713
DOI: 10.21136/MB.2011.141454
Date available: 2011-03-31T11:31:21Z
Last updated: 2020-07-29
Stable URL:
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Reference: [2] Aliprantis, C. D., Burkinshaw, O.: Positive Operators.Reprint of the 1985 original. Springer, Dordrecht (2006). Zbl 1098.47001, MR 2262133
Reference: [3] Dodds, P. G.: o-weakly compact mappings of Riesz spaces.Trans. Amer. Math. Soc. 214 (1975), 389-402. Zbl 0313.46011, MR 0385629
Reference: [4] Meyer-Nieberg, P.: Banach Lattices.Universitext. Springer, Berlin (1991). Zbl 0743.46015, MR 1128093
Reference: [5] Wickstead, A. W.: Converses for the Dodds-Fremlin and Kalton-Saab Theorems.Math. Proc. Camb. Phil. Soc. 120 (1996), 175-179. Zbl 0872.47018, MR 1373356, 10.1017/S0305004100074752


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