Open AccessLipschitz integral operators represented by vector measures
Author(s) -
Elhadj Dahia,
Khaled Hamidi
Publication year - 2021
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 13
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2021.15061
Subject(s) - mathematics , lipschitz continuity , pure mathematics , banach space , hausdorff measure , factorization , hausdorff space , fourier integral operator , measure (data warehouse) , discrete mathematics , operator theory , hausdorff dimension , algorithm , database , computer science
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.