Lipschitz integral operators represented by vector measures

• Dahia, Elhadj ^[1] ; Hamidi, Khaled ^[2]
  1. [1] Ecole Normale Supérieure de Bousaada
  2. [2] University of Mohamed El-Bachir El-Ibrahimi ; University of M’sila
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 2, 2021, págs. 367-383
• Idioma: inglés
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• Resumen

  • 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 vectormeasure 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.