MODSTABBAN
Model theoretic stability for Banach spaces
| Coordinatore | THE OPEN UNIVERSITY*
Organization address
address: RAVUZKI 108 contact info |
| Nazionalità Coordinatore | Israel [IL] |
| Totale costo | 100˙000 € |
| EC contributo | 100˙000 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-2012-CIG |
| Funding Scheme | MC-CIG |
| Anno di inizio | 2013 |
| Periodo (anno-mese-giorno) | 2013-06-01 - 2018-10-30 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
THE OPEN UNIVERSITY*
Organization address
address: RAVUZKI 108 contact info |
IL (RAANANA) | coordinator | 100˙000.00 |
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Obiettivo del progetto (Objective)
'The proposed project will advance our knowledge in the field of model theory and its applications to functional analysis and Banach space geometry. The research will mobilize recently developed powerful model theoretic techniques in order to throw more light on important and basic questions in Banach space theory. The project will enhance exchange of ideas and techniques between different areas of mathematics, especially stability theory within model theory and Banach space theory.
Specifically, we propose to explore connections between model theoretic stability and geometric structure of a fixed Banach space, as well as an elementary class of Banach spaces. The main idea is that stability leads to deeper understanding of spreading models in the ultra-powers of a structure. The project will continue and expand the work of Krivine and Maurey, who proved that stability implies the existence of an almost isometric copy of an l_p space. One of the questions we are going to address is whether weaker versions of stability entail the existence of isomorphic copies of basic sequence spaces.
Another question that we will investigate has to do with the phenomenon of categoricity. A class of Banach spaces is called categorical if it has a unique structure (up to isometry) of some uncountable density. We have recently shown that any such class is strongly related to the class of Hilbert spaces, affirming a 35-year old Henson's Conjecture. Recent developments suggest stronger geometric forms of the conjecture, which we will address.
In addition, we propose to investigate an analogous conjecture for categoricity under isomorphisms (instead of isometries), which is a much more challenging problem. However, given recent progress in 'geometric stability theory' in the context of Banach spaces (due to the my collaborators and myself), we are confident that many interesting results are within reach now.'