Interpolation, twisted sums and borelian classes of Banach Spaces

• Grant number: 14/25900-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): May 01, 2015
• Effective date (End): March 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Acordo de Cooperação: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Valentin Raphael Henri Ferenczi
• Grantee: Wilson Albeiro Cuellar Carrera
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The main objective of this post doctoral project is to continue with the research of the candidate during his PhD about twisted sums and complex structures on Banach spaces. We also are interested in a new direction of research, mainly about the classification and description of some equivalence relations in the category of separable Banach spaces.We integrate to the research new methods obtained from the interpolation theory and descriptive set theory to treat questions related to the problems of complex structures on the Kalton-Peck space and its hyperplanes; and criteria for singularity and non triviality of twisted sums 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)

CASTILLO, JESUS M. F.; CUELLAR, WILSON; FERENCZI, VALENTIN; MORENO, YOLANDA. COMPLEX STRUCTURES ON TWISTED HILBERT SPACES. Israel Journal of Mathematics, v. 222, n. 2, p. 787-814, OCT 2017. (10/17512-6, 15/17216-1, 14/25900-7, 13/11390-4)

CUELLAR CARRERA, W.. NON-ERGODIC BANACH SPACES ARE NEAR HILBERT. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 370, n. 12, p. 8691-8707, DEC 2018. (14/25900-7)