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In this article we continue studying the ideals of two-Lipschitz operators.We prove a lot of important results concerning this class of non-linearmappings. We propose a defnition of the injective hull of a two-Lipschitzoperator ideal which extend that introduced by Stephani for the linear case.There are different ways of constructing an ideal of multilinear mappings froma given operator ideal. In this work we fill this gap by developing twotechniques to generate two-Lipschitz operator ideals from given Lipschitzoperator ideals.

Some further results on ideals of two-Lipschitz operators between mertic and Banach spaces part I