Lipschitz operators represented by vector measures

Abstract

In this memory,the concept of Lipschitz Pietsch-p-integral operators, where (1 6 p < 1). These operators are defined as Lipschitz mappings between a metric space and a Banach space. They can be represented by an integral with respect to a vector measure defined on a suitable compact Hausdorff space. We show that this type of operator fits into the theory of composition Banach Lipschitz operator ideals. and a rich factorization theory for these operators, which provides a lot of information about them. This factorization theory is based on the classical Banach spaces C(K); Lp( ;K) and L1( ;K), where K is a compact Hausdorff space. We believe that this work provides a new and useful perspective on Lipschitz Pietsch-p-integral operators. We hope that it will be of interest to researchers in functional analysis and operator theory.