The Lipschitz injective hull of Lipschitz operator ideals and applications

2020 ◽  
Vol 14 (3) ◽  
pp. 1241-1257 ◽  
Author(s):  
Dahmane Achour ◽  
Elhadj Dahia ◽  
Pablo Turco
Keyword(s):  
Injective Hull ◽  
Operator Ideals ◽  
Lipschitz Operator

scholarly journals Lipschitz integral operators represented by vector measures

2021 ◽  
Vol 22 (2) ◽  
pp. 367
Author(s):  
Elhadj Dahia ◽  
Khaled Hamidi
Keyword(s):  
Hausdorff Space ◽  
Integral Operators ◽  
Operator Ideals ◽  
Weakly Compact ◽  
Vector Measures ◽  
Factorization Theory ◽  
Weakly Compact Operator ◽  
Lipschitz Operator ◽  
The Relationship ◽  
Lipschitz Operators

<p>In this paper we introduce the concept of Lipschitz Pietsch-p-integral <br />mappings, (1≤p≤∞), between a metric space and a Banach space. We represent these mappings by an integral with respect to a vector<br />measure defined on a suitable compact Hausdorff space, obtaining in this way a rich factorization theory through the classical Banach spaces C(K), L_p(μ,K) and L_∞(μ,K). Also we show that this type of operators fits in the theory of composition Banach Lipschitz operator ideals. For p=∞, we characterize the Lipschitz Pietsch-∞-integral mappings by a factorization schema through a weakly compact operator. Finally, the relationship between these mappings and some well known Lipschitz operators is given.</p>

scholarly journals Lipschitz operator ideals and the approximation property

2016 ◽  
Vol 436 (1) ◽  
pp. 217-236 ◽  
Author(s):  
D. Achour ◽  
P. Rueda ◽  
E.A. Sánchez-Pérez ◽  
R. Yahi
Keyword(s):  
Approximation Property ◽  
Operator Ideals ◽  
Lipschitz Operator

Two-Lipschitz operator ideals

2020 ◽  
Vol 491 (2) ◽  
pp. 124346
Author(s):  
Khaled Hamidi ◽  
Elhadj Dahia ◽  
Dahmane Achour ◽  
Abdelhamid Tallab
Keyword(s):  
Operator Ideals ◽  
Lipschitz Operator

Injective Dual Banach Spaces and Operator Ideals

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Raffaella Cilia ◽  
Joaquín M. Gutiérrez
Keyword(s):  
Banach Spaces ◽  
Operator Ideals

Nonlinear equations in soliton physics and operator ideals

Nonlinearity ◽  
1999 ◽  
Vol 12 (2) ◽  
pp. 333-364 ◽  
Author(s):  
B Carl ◽  
C Schiebold
Keyword(s):  
Nonlinear Equations ◽  
Operator Ideals

scholarly journals Small operator ideals on the Schlumprecht and Schreier spaces

2021 ◽  
pp. 109156
Author(s):  
Antonis Manoussakis ◽  
Anna Pelczar-Barwacz
Keyword(s):  
Operator Ideals

Duality of the distance to closed operator ideals

2003 ◽  
Vol 133 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Hans-Olav Tylli
Keyword(s):  
Banach Spaces ◽  
Closed Operator ◽  
Operator Ideal ◽  
Linear Operators ◽  
Distance Functions ◽  
Approximation Properties ◽  
Operator Ideals ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Special Operator

Special operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist(S*, I(F*, E*)) and S ↦ dist(S, I*(E, F)) are uniformly comparable in each space L(E, F) of bounded linear operators. Here, I*(E, F) = {S ∈ L(E, F) : S* ∈ I(F*, E*)} stands for the adjoint ideal of the closed operator ideal I for Banach spaces E and F. Counterexamples are obtained for many classical surjective or injective Banach operator ideals I by solving two resulting ‘asymmetry’ problems for these operator-ideal APs.

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