Lipschitz operators represented by vector measures
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Date
2023-06-10
Journal Title
Journal ISSN
Volume Title
Publisher
University of M'sila
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.
Description
Keywords
Vector measures„ Arens-Eells space,Lipschitz operator,Lipschitz operator ideals,Lipschitz mapping, factorization of operators,