Abstract:
Many classes of linears operator ideals for example the p- summing, p- nuclear, p- integral, compact and weakly compact operators have been developed and studied in the lipschitz setting by several authors.
In this thesis we introduce the notion of lipschitz operator ideal and some methods of constructions.
We show that a number of examples of classes of lipschitz maps that have appeared in the literature fall within this notion of Lipschitz operator ideal, New classes of Lips- chitz operators ideals are introduced and study in our thesis, namely the strongly Lipschitz p- summing operator and ( p, o ) - absolutely Lipschitz operator, as an ap- plication we studied the approximation property for lipschitz operator ideats. We finish this thesis by studying the factorization of Lipschitz operators on Banach function spaces.
