New directions in the Theory of Complexity for Banach Spaces

• Grant number: 09/05879-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: October 08, 2009
• End date: November 07, 2009
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Eloi Medina Galego
• Grantee: Eloi Medina Galego
• Visiting researcher: Jesús María Fernández Castillo
• Visiting researcher institution: Universidad de Extremadura, Badajoz (UEx), Spain
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Our project is related to the following natural question on Geometry of Banach spaces. Fixed a subspace $Y$ of a Banach space $X$, how many different positions does $Y$ admit into $X$?The study of this question requires to apply some concepts and results of theory of complexity of Borelian relations as well as some results of the classical theory of Banach spaces.We will try to use some very recent results on these topics to obtain the answer to the above question in the case of some Banach spaces $Y$ and $X$. (AU)