On the composition ideals of Lipschitz mappings

TL;DR

This paper explores the structure of Lipschitz mappings that factor through operator ideals, introduces Lipschitz cross-norms from tensor norms, and proposes a new class called strictly Lipschitz p-summing.

Contribution

It introduces the concept of strictly Lipschitz p-summing mappings and constructs Lipschitz cross-norms from tensor norms to represent Lipschitz mapping classes.

Findings

Defined strictly Lipschitz p-summing mappings.

Constructed Lipschitz cross-norms from tensor norms.

Provided a framework for representing Lipschitz mapping classes.

Abstract

We study in this paper some property of Lipschitz mappings which admit factorization through an operator ideal. We try to construct Lipschitz cross-norms from known tensor norms in order to represent certain classes of Lipschitz mappings. Inspired by the definition of p-summing linear operators we introduce a new concpet in the the category of Lipschitz mappings that is called strictly Lipschitz p-summing.