Combinatorial methods in Banach Spaces

• Grant number: 12/24463-7
• Support Opportunities: Regular Research Grants
• Start date: March 01, 2013
• End date: February 28, 2015
• 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

Our purpose is to apply combinatorial methods to obtain results concerning Banach spaces. In particular, we are interested in uncountable structures like biorthogonal systems and basic sequences, in the dual space and in the space of operators of a Banach $C(K)$-space and in the impact of combinatorial problems in the space $\ell_\infty/c_0$. The forcing, which we used in the major part of our previous research works, is our main tool, but we consider also modern principles which have been proved to be powerful in problems in Analysis recently. (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, C.; LOPEZ-ABAD, J.; TODORCEVIC, S.. Homogeneous families on trees and subsymmetric basic sequences. ADVANCES IN MATHEMATICS, v. 334, p. 322-388, AUG 20 2018. (15/26654-2, 12/24463-7, 13/24827-1)

BRECH, CHRISTINA; KOSZMIDER, PIOTR. AN ISOMETRICALLY UNIVERSAL BANACH SPACE INDUCED BY A NON-UNIVERSAL BOOLEAN ALGEBRA. Proceedings of the American Mathematical Society, v. 144, n. 5, p. 2029-2036, MAY 2016. (12/24463-7)