On the duality problem for weakly compact, strictly singular operators

2005 ◽  
Vol 28 (1) ◽  
pp. 37-38
Author(s):  
Manuel González
Keyword(s):  
Weakly Compact ◽  
Singular Operators ◽  
Strictly Singular ◽  
Duality Problem

scholarly journals A class of Banach spaces with few non-strictly singular operators

2005 ◽  
Vol 222 (2) ◽  
pp. 306-384 ◽  
Author(s):  
S.A. Argyros ◽  
J. Lopez-Abad ◽  
S. Todorcevic
Keyword(s):  
Banach Spaces ◽  
Singular Operators ◽  
Strictly Singular

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

Domination by Positive Strictly Singular Operators

2002 ◽  
Vol 66 (2) ◽  
pp. 433-452 ◽  
Author(s):  
Julio Flores ◽  
Francisco L. Hernández
Keyword(s):  
Singular Operators ◽  
Strictly Singular

scholarly journals Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Marian Nowak
Keyword(s):  
Continuous Functions ◽  
Linear Operators ◽  
Strict Topology ◽  
Weakly Compact ◽  
Completely Continuous ◽  
Completely Regular ◽  
Strictly Singular ◽  
Continuous Operators ◽  
Bounded Continuous Functions ◽  
The Relationship

LetXbe a completely regular Hausdorff space and letE,·Eand(F,·F)be Banach spaces. LetCb(X,E)be the space of allE-valued bounded, continuous functions onX, equipped with the strict topologyβσ. We study the relationship between important classes of(βσ,·F)-continuous linear operatorsT:Cb(X,E)→F(strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived.

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.

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