Bases and universality in Banach spaces

• Grant number: 10/12638-1
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2010
• End date: January 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Christina Brech
• Grantee: Christina Brech
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project, our main purpose is to study the relation between geometrical properties of Banach spaces with two structures: bases and universal spaces. Regarding bases, we consider two of its main versions: Schauder bases and biorthogonal systems. Even if they have been largely studied since through history, there is still much to understand about their relation to the spaces'structure. In what concerns universal spaces, we are interested both in the classical notion and in other ones like, for example, the universal disposition for separable spaces. For this research, we propose the use of combinatorial methods, which are essential to construct examples which attest the richness of the theory and also useful in proving results in the modern theory of Banach spaces. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BRECH, CHRISTINA; KOSZMIDER, PIOTR. ON UNIVERSAL SPACES FOR THE CLASS OF BANACH SPACES WHOSE DUAL BALLS ARE UNIFORM EBERLEIN COMPACTS. Proceedings of the American Mathematical Society, v. 141, n. 4, p. 1267-1280, APR 2013. (10/12638-1)