Lipschitz closed injective ideals and interpolative Lipschitz ideals

Abstract

In this memoir, we study two methods for generating a Lipschitz operator ideal from a given Lipschitz ideal Zip. The first method is the closed injective hull procedure, denoted by Izip The second method is the interpolative procedure, denoted by (Lip). We investigate various properties related to both procedures and study the relationship between the resulting ideals, establishing the following inclusion:

IC(ILip) CILip

For the concrete class (Пpo Lipo), consisting of Lipschitz operators whose linearization is a (po)-absolutely continuous linear operator, we obtain Pietsch-type domination and factorization theorems.