Bulletin of the Belgian Mathematical Society - Simon Stevin

Weak compactness of AM-compact operators

Belmesnaoui Aqzzouz, Jawad H'Michane, and Othman Aboutafail

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Abstract

We characterize Banach lattices under which each AM-compact operator (resp. the second power of a positive AM-compact operator) is weakly compact. Also, we give some interesting results about b-weakly compact operators and operators of strong type B.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 2 (2012), 329-338.

Dates
First available in Project Euclid: 24 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1337864276

Digital Object Identifier
doi:10.36045/bbms/1337864276

Mathematical Reviews number (MathSciNet)
MR2977235

Zentralblatt MATH identifier
1253.46027

Subjects
Primary: 46A40: Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42] 46B40: Ordered normed spaces [See also 46A40, 46B42] 46B42: Banach lattices [See also 46A40, 46B40]

Keywords
weakly compact operator AM-compact operator b-weakly compact operator operator of strong type B Banach lattice order continuous norm KB-space reflexive space

Citation

Aqzzouz, Belmesnaoui; H'Michane, Jawad; Aboutafail, Othman. Weak compactness of AM-compact operators. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 2, 329--338. doi:10.36045/bbms/1337864276. https://projecteuclid.org/euclid.bbms/1337864276


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