Three non-linear problems on normed spaces

  1. García Pacheco, Francisco Javier
Dirigée par:
  1. Richard M. Aron Directeur/trice

Université de défendre: Kent State University

Fecha de defensa: 18 août 2007

Jury:
  1. Per H. Enflo Rapporteur
  2. Andrew Tonge Rapporteur

Type: Thèses

DIALNET

Résumé

In this dissertation, we will study the following three non-linear problems: 1. The lineability problem for functionals. 2. The minimum-norm problem for translations. 3. The Banach-Mazur conjecture for rotations. As far as we know, all of them are currently open, and we believe that any approach to their solutions will constitute a work of great interest to the mathematical community. In this dissertation, we obtain progresses that lead to partial solutions of these problems.