Combinatorial aspects of nonseparable Banach spaces structure

• Grant number: 07/08213-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2008
• End date: March 31, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jorge Tulio Mujica Ascui
• Grantee: Christina Brech
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 06/02378-7 - Infinite Dimensional Analysis, AP.TEM

Abstract

The purpose of this post-doctoral project is to continue the research done during the Ph.D. on renormings of nonseparable C(K) Banach spaces. To solve problems of the structure theory of Banach spaces, we use combinatorial methods such as forcing and transfinite induction, as well as combinatorial principles such as the continuum hypothesis. We are specially interested in Asplund spaces, their possible renormings and the existence of other geomtrical structures inside them. Among the problems we plan to work with, there are classical problems and problems which were partially solved during the Ph.D.

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 Banach spaces of density continuum. Israel Journal of Mathematics, v. 190, n. 1, p. 93-110, AUG 2012. (06/02378-7, 07/08213-2)

AVILES, ANTONIO; BRECH, CHRISTINA. A Boolean algebra and a Banach space obtained by push-out iteration. Topology and its Applications, v. 158, n. 13, p. 1534-1550, AUG 15 2011. (06/02378-7, 07/08213-2)