معلومات المقرر

This course was given in the first semester of 2020-2021 at the university of M'sila. The text is intended for the students of M₂. The main theme of this course is to give an introduction to the non linear summing operators in the domain of "the nonlinear geometry of Banach spaces". We treat and study in chapter I, the Lipschitz functions between metric spaces and the Lipschitz dual space of a metric space. This space is a conjugate Banach space. We study the predual and their properties. Chapter two is devoted to the notion of Lipschitz p-summing functions introduced by Farmer and Johnson. We end this by giving the non linear Grothendieck's theorem. In chapter three, We introduce and study some other classes of summability and their connections. I have tried to make this course fairly complete and comprehensive. For this, I recommend essentially the excellent book of Weaver and the papers of Farmer-Johnson and Godfroy-Kalton.