Approximation properties in terms of Lipschitz maps

Abstract

In this work , we dealt with one of the most important topics of functional analysis, which is the approximation properties related to the ideals of Lipschitz and linear operators.. We have tried, as much as possible , with a very modest effort to become familiar with the most important definitions, theorems and properties of all chapters of this memory . In the first chapter, we recall briefly the space of Lipschitz functions, Arens–Eells and Lipschitz operator ideals. Chapter two devoted to study the approximation property for Banach spaces. The third chapter devoted to study the approximation property for Lipschitz operator ideals.