Three non-linear problems on normed spaces

  1. García Pacheco, Francisco Javier
Supervised by:
  1. Richard M. Aron Director

Defence university: Kent State University

Fecha de defensa: 18 August 2007

Committee:
  1. Per H. Enflo Committee member
  2. Andrew Tonge Committee member

Type: Thesis

DIALNET

Abstract

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.