Three non-linear problems on normed spaces
- Richard M. Aron Doktorvater/Doktormutter
Universität der Verteidigung: Kent State University
Fecha de defensa: 18 von August von 2007
- Per H. Enflo Vocal
- Andrew Tonge Vocal
Art: Dissertation
Zusammenfassung
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.