Banach spaces with various complex structures

• Grant number: 10/17512-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2011
• End date: February 28, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• 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
• Associated scholarship(s): 12/00631-8 - Methods of set theory in the theory of complex structures, BE.EP.DR

Abstract

This research project is a study of complex structures on real Banach spaces, to be developed during the candidate's doctoral studies at the Institute of Mathematics and Statistics (IME-USP). The candidate will study the spaces successively built by Bourgain, Kalton and Ferenczi, which are examples of Banach spaces with at least two distinct complex structures. The first goal will be to determine the exact number of different complex structures which have each of the first two examples. From the different methods developed for studying these three spaces and the study of Fredholm theory, the candidate will try to define a space with just a countable infinite number of complex structures. In addition, the student will use the descriptive set theory applied to Banach space theory, to study the number of complex structures in a given space, in the framework of equivalence relations on Polish spaces.

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)

CARRERA, W. CUELLAR. A Banach space with a countable infinite number of complex structures. JOURNAL OF FUNCTIONAL ANALYSIS, v. 267, n. 5, p. 1462-1487, SEP 1 2014. (10/17512-6, 12/00631-8)

CUELLAR CARRERA, W.. Complex Structures on Banach spaces with a subsymmetric basis. Journal of Mathematical Analysis and Applications, v. 440, n. 2, p. 624-635, AUG 15 2016. (10/17512-6)

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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CARRERA, Wilson Albeiro Cuellar. Banach spaces with various complex structures. 2015. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.