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New directions in the Theory of Complexity for Banach Spaces

Grant number: 09/05879-5
Support type:Research Grants - Visiting Researcher Grant - International
Duration: October 08, 2009 - 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
Home 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)