Partial orders and its applications to the geometry of Banach spaces

• Grant number: 11/15129-3
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2012
• End date: August 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Christina Brech
• Grantee: Clayton Suguio Hida
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 13/01609-9 - Constructions of C(K) spaces, BE.EP.MS

Abstract

In this project we propose the study of some methods based on partial orders, which can be applied to the topology and the geometry of Banach spaces. Among these methods, we focus on some axioms like Martin axiom, proper forcing axiom and Martin maximum. We consider aswell the forcing method, which was introduced by Cohen in the XXth century to solve the problem on the continuum hypothesis. On one hand, this methods allow us to construct compact Hausdorff spaces K with interesting properties, which lead us to interesting Banach spaces C(K). On the other hand, by the same methods one can get general results on the topology and the geometry of Banach spaces. We would like to mention that the chosen methods were used in recent results, as one can find out from the references of this project.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

HIDA, Clayton Suguio. Biorthogonal systems in Banach spaces C(K). 2014. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.