Lipschitz integral operators represented by vector measures


  • Elhadj Dahia Ecole Normale Supérieure de Bousaada
  • Khaled Hamidi University of Mohamed El-Bachir El-Ibrahimi ; University of M’sila



Lipschitz Pietsch-p-integral operators, Lipschitz strictly p-integral operators, vector measure representation


In this paper we introduce the concept of Lipschitz Pietsch-p-integral
mappings, (1≤p≤∞), between a metric space and a Banach space. We represent these mappings by an integral with respect to a vector
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.


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Author Biographies

Elhadj Dahia, Ecole Normale Supérieure de Bousaada

Laboratoire de Mathématiques et Physique Appliquées

Khaled Hamidi, University of Mohamed El-Bachir El-Ibrahimi ; University of M’sila

Department of Mathematics ; Laboratoire d’Analyse Fonctionnelle et Géométrie des Espaces


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How to Cite

E. Dahia and K. Hamidi, “Lipschitz integral operators represented by vector measures”, Appl. Gen. Topol., vol. 22, no. 2, pp. 367–383, Oct. 2021.



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