Analytic families of Banach spaces

• Grant number: 21/13401-0
• Support Opportunities: Scholarships abroad - Research
• Start date: August 08, 2022
• End date: August 07, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Willian Hans Goes Corrêa
• Grantee: Willian Hans Goes Corrêa
• Host Investigator: Jesús María Fernández Castillo
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universidad de Extremadura, Badajoz (UEx), Spain

Abstract

The study of interpolation theory motivates the concept of analytic family. These families try to capture the notion of an analytic function which values are Banach spaces, and they arise naturally when we study the complex interpolation methods for pairs and families of Banach spaces. We are interested in what corresponds to the process of differentiation of those families, which generates the so-called derived spaces. This process is closely linked to the homological theory of Banach spaces, as the derived spaces are twisted sums of the spaces that compose the family. Ideally, properties of the analytic family should induce properties of the derived spaces. Likewise, properties of the derived spaces should imply corresponding properties for the analytic families. Thus, this project proposes the study of how properties of derived spaces generated by analytic families of Banach spaces are related to properties of those families. (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)

SANCHEZ, FELIX CABELLO; CASTILLO, JESUS M. F.; CORREA, WILLIAN H. G.. Higher order derivatives of analytic families of Banach spaces. STUDIA MATHEMATICA, v. N/A, p. 53-pg., 2023-07-20. (18/03765-1, 16/25574-8, 21/13401-0)