scholarly journals Weak Compactness of Almost Limited Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Aziz Elbour ◽  
Nabil Machrafi ◽  
Mohammed Moussa
Keyword(s):  
Banach Lattice ◽  
Compact Operators ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Weakly Compact Operators ◽  
Limited Operator ◽  
Almost Limited Operator ◽  
The Relationship ◽  
Order Continuous

This paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that ifFis aσ-Dedekind complete Banach lattice, then every almost limited operatorT:E→Fis weakly compact if and only ifEis reflexive or the norm ofFis order continuous. Also, we show that ifEis aσ-Dedekind complete Banach lattice, then the square of every positive almost limited operatorT:E→Eis weakly compact if and only if the norm ofEis order continuous.

scholarly journals THE DUALITY PROBLEM FOR THE CLASS OF ORDER WEAKLY COMPACT OPERATORS

2009 ◽  
Vol 51 (1) ◽  
pp. 101-108 ◽  
Author(s):  
BELMESNAOUI AQZZOUZ ◽  
JAWAD HMICHANE
Keyword(s):  
Necessary Conditions ◽  
Compact Operators ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Weakly Compact Operators ◽  
Sufficient And Necessary Conditions ◽  
Duality Problem

AbstractWe study the duality problem for order weakly compact operators by giving sufficient and necessary conditions under which the order weak compactness of an operator implies the order weak compactness of its adjoint and conversely.

Weak compactness of almost L-weakly and almost M-weakly compact operators

2020 ◽  
pp. 1-10
Author(s):  
Farid Afkir ◽  
Khalid Bouras ◽  
Aziz Elbour ◽  
Safae El Filali
Keyword(s):  
Compact Operators ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Weakly Compact Operators

scholarly journals Quantitative approach to weak noncompactness in the polygon interpolation method

2004 ◽  
Vol 69 (1) ◽  
pp. 49-62 ◽  
Author(s):  
Andrzej Kryczka
Keyword(s):  
Interpolation Method ◽  
Compact Operators ◽  
Weak Compactness ◽  
Quantitative Approach ◽  
Weakly Compact ◽  
Weakly Compact Operators

We study a quantitative approach to weak noncompactness of operators under the Cobos-Peetre polygon interpolation method for Banach N-tuples. In the case of operators acting between two J-spaces or two K-spaces obtained by this method we prove logarithmically convex-type inequalities for certain operator seminorm vanishing on the subspace of weakly compact operators. Geometrically speaking, in these estimates only some triangles inscribed in the polygon are involved. For operators acting from a J-space to a K-space we prove logarithmically convex-type estimates where all polygon vertices are included. In particular, the estimates obtained here give the new proofs of the results showing the relation between distribution of weakly compact operators among polygon vertices and weak compactness of operators under interpolation.

On the weak compactness of b-weakly compact operators

Positivity ◽  
2009 ◽  
Vol 14 (1) ◽  
pp. 75-81 ◽  
Author(s):  
Belmesnaoui Aqzzouz ◽  
Aziz Elbour
Keyword(s):  
Compact Operators ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Weakly Compact Operators

On the weak compactness of order weakly compact operators

2012 ◽  
Vol 78 (3-4) ◽  
pp. 559-567
Author(s):  
Belmesnaoui Aqzzouz ◽  
Aziz Elbour
Keyword(s):  
Compact Operators ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Weakly Compact Operators

scholarly journals On the Lattice Properties of Almost L-Weakly and Almost M-Weakly Compact Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Barış Akay ◽  
Ömer Gök
Keyword(s):  
Linear Span ◽  
Compact Operators ◽  
Approximation Properties ◽  
Order Continuous Norm ◽  
Continuous Norm ◽  
Weakly Compact ◽  
Domination Property ◽  
Weakly Compact Operators ◽  
Lattice Approximation ◽  
Order Continuous

We establish the domination property and some lattice approximation properties for almost L-weakly and almost M-weakly compact operators. Then, we consider the linear span of positive almost L-weakly (resp., almost M-weakly) compact operators and give results about when they form a Banach lattice and have an order continuous norm.

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