Erratum to: Compactness properties for operators dominated by AM-compact operators [PDF]
Proceedings of the American Mathematical Society, 2009 In [ibid. 135, No. 4, 1151--1157 (2007; Zbl 1118.47029)], the authors have characterized Banach lattices such that operators dominated by AM-compact operators are AM-compact; but there was an error in the proof of this characterization. In this note, they give a new and correct proof by using a new lemma.
Belmesnaoui Aqzzouz, Aziz Elbour
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Weak compactness of AM-compact operators [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Belmesnaoui Aqzzouz +2 more
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On the modulus of disjointness-preserving operators and $b$ - $AM$ -compact operators on Banach lattices [PDF]
Annals of Functional Analysis, 2017 We study several properties of the modulus of order bounded disjointness-preserving operators. We show that, if T is an order bounded disjointness-preserving operator, then T and |T| have the same compactness property for several types of compactness.
Kazem Haghnezhad Azar, Razi Alavizadeh
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The Duality Problem for the Class of AM-Compact Operators on Banach Lattices [PDF]
Canadian Mathematical Bulletin, 2008 AbstractWe prove the converse of a theorem of Zaanen about the duality problem of positive AM-compact operators.
Belmesnaoui Aqzzouz +2 more
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Compactness properties of operators dominated by AM-compact operators [PDF]
Proceedings of the American Mathematical Society, 2006 Based on work of Fremlin, the authors study the domination problem for the class of AM-compact oeprators. Let \(E\) be an arbitrary Banach lattice and let \(S\) and \(T\) be two operators from \(E\) into \(E\) such that \(0\leq S\leq T\) and \(T\) is AM-compact. Then it is shown that \(S^2\) is AM-compact.
Belmesnaoui Aqzzouz +2 more
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Domination problem for AM-compact abstract Uryson operators
Archiv der Mathematik, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
V. P. Orlov, Marat Pliev, Dmitry Rode
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Erratum: The Duality Problem For The Class of AM-Compact Operators On Banach Lattices [PDF]
Canadian Mathematical Bulletin, 2011 Belmesnaoui Aqzzouz
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On linear sections of orthogonally additive operators
Математичні Студії, 2022 Our first result asserts that, for linear regular operators acting from a Riesz space with the principal projection property to a Banach lattice with an order continuous norm, the $C$-compactness is equivalent to the $AM$-compactness. Next we prove that,
A. Gumenchuk, I. Krasikova, M. Popov
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Application of ${\rm (L)$ sets to some classes of operators} [PDF]
Mathematica Bohemica, 2016 The paper contains some applications of the notion of $L$ sets to several classes of operators on Banach lattices. In particular, we introduce and study the class of order ${\rm (L)$-Dunford-Pettis operators, that is, operators from a Banach space into a
Kamal El Fahri +3 more
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Difference of composition operators on weighted Bergman spaces over the half-plane
Journal of Inequalities and Applications, 2016 Recently, the bounded, compact and Hilbert-Schmidt difference of composition operators on the Bergman spaces over the half-plane are characterized in (Choe et al. in Trans. Am. Math. Soc., 2016, in press).
Maocai Wang, Changbao Pang
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