Can I read Some aspects of the geometry of Lipschitz free spaces [PhD thesis] on EtoBox?

Some aspects of the geometry of Lipschitz free spaces [PhD thesis] by Petitjean, C. is a nonfiction available to read on EtoBox.

What is Some aspects of the geometry of Lipschitz free spaces [PhD thesis] about?

Some aspects of the geometry of Lipschitz free spaces.First and foremost, we give the fundamental properties of Lipschitz free spaces. Then, we prove that the canonical image of a metric space M is weakly closed in the associated free space F(M). We prove a similar result for the set of molecules.In the second chapter, we study the circumstances in which F(M) is isometric to a dual space. In particular, we generalize a result due to Kalton on this topic. Subsequently, we focus on uniformly discrete metric spaces and on metric spaces originating from p-Banach spaces.In the next chapter, we focus on l1-like properties. Among other things, we prove that F(M) has the Schur property provided the space of little Lipschitz functions is 1-norming for F(M). Under additional assumptions, we manage to embed F(M) into an l1-sum of finite dimensional spaces.In the fourth chapter, we study the extremal structure of F(M). In particular, we show that any preserved extreme point in the unit ball of a free space is a denting point. Moreover, if F(M) admits a predual, we obtain a precise description of its extremal structure.The fifth chapter deals with vector-valued Lipschitz functions.We generalize

Who reads Some aspects of the geometry of Lipschitz free spaces [PhD thesis]?

Author

Petitjean, C.

Publisher

Université de Bourgogne

Published

2018

Language

EN

Category

nonfiction

Subjects

Mathematics, Functional Analysis, Stem