Interval-Bounded Operators And Order-Weakly Compact Operators Of Riesz Spaces

1998 ◽  
Vol 31 (4) ◽  
Author(s):  
Zafer Ercan
Keyword(s):  
Compact Operators ◽  
Bounded Operators ◽  
Weakly Compact ◽  
Riesz Spaces ◽  
Weakly Compact Operators

Sur Les M-Ideaux Dans Certains Espaces D′Operateurs Et L′Approximation Par Des Operateurs Compacts

1980 ◽  
Vol 23 (4) ◽  
pp. 401-411 ◽  
Author(s):  
H. Fakhoury
Keyword(s):  
Best Approximation ◽  
Compact Operators ◽  
Approximation Properties ◽  
Bounded Operators ◽  
Weakly Compact ◽  
The Best Approximation ◽  
Weakly Compact Operators

SommaireIt is shown that if V=C(X) or V = L1(μ) then the subspace of compact (resp. weakly compact) operators from V into itself is not an M-ideal in the space of bounded operators. This is the contrary to what happens when V= Co(ℕ) or lp(ℕ). The main result is proved via the best approximation properties of M-ideals and some results concerning norm one projections in C(X) and L1(μ) are deduced from this fact.

scholarly journals Uniformly factoring weakly compact operators and parametrised dualisation

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Antunes ◽  
K. Beanland ◽  
B. M. Braga
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Borel Subset ◽  
Compact Operators ◽  
Schauder Basis ◽  
Bounded Operators ◽  
Weakly Compact ◽  
Weakly Compact Operator ◽  
Borel Map ◽  
Weakly Compact Operators

Abstract This article deals with the problem of when, given a collection $\mathcal {C}$ of weakly compact operators between separable Banach spaces, there exists a separable reflexive Banach space Z with a Schauder basis so that every element in $\mathcal {C}$ factors through Z (or through a subspace of Z). In particular, we show that there exists a reflexive space Z with a Schauder basis so that for each separable Banach space X, each weakly compact operator from X to $L_1[0,1]$ factors through Z. We also prove the following descriptive set theoretical result: Let $\mathcal {L}$ be the standard Borel space of bounded operators between separable Banach spaces. We show that if $\mathcal {B}$ is a Borel subset of weakly compact operators between Banach spaces with separable duals, then for $A \in \mathcal {B}$ , the assignment $A \to A^*$ can be realised by a Borel map $\mathcal {B}\to \mathcal {L}$ .

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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