The duality problem for the Class of b-weakly compact operators

Positivity ◽  
2009 ◽  
Vol 13 (4) ◽  
pp. 683-692 ◽  
Author(s):  
Belmesnaoui Aqzzouz ◽  
Aziz Elbour ◽  
Jawad Hmichane
Keyword(s):  
Compact Operators ◽  
Weakly Compact ◽  
Weakly Compact Operators ◽  
Duality Problem

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.

scholarly journals Dual functors and the Radon-Nikodym property in the category of Banach spaces

1979 ◽  
Vol 27 (4) ◽  
pp. 479-494 ◽  
Author(s):  
John Wick Pelletier
Keyword(s):  
Banach Spaces ◽  
Direct Limit ◽  
Integral Operators ◽  
Compact Operators ◽  
Property A ◽  
Weakly Compact ◽  
Nikodym Property ◽  
Weakly Compact Operators

AbstractThe notion of duality of functors is used to study and characterize spaces satisfying the Radon-Nikodym property. A theorem of equivalences concerning the Radon-Nikodym property is proved by categorical means; the classical Dunford-Pettis theorem is then deduced using an adjointness argument. The functorial properties of integral operators, compact operators, and weakly compact operators are discussed. It is shown that as an instance of Kan extension the weakly compact operators can be expressed as a certain direct limit of ordinary hom functors. Characterizations of spaces satisfying the Radon-Nikodym property are then given in terms of the agreement of dual functors of the functors mentioned above.

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