Interpolation theory and geometry of Banach Spaces

• Grant number: 23/06973-2
• Support Opportunities: Research Grants - Young Investigators Grants
• Start date: June 01, 2024
• End date: May 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Willian Hans Goes Corrêa
• Grantee: Willian Hans Goes Corrêa
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 24/20723-1 - Copies of c0 in the set of strongly norm-attaining Lipschitz functions, BP.MS; 24/22796-6 - The reverse Brunn-Minkowski inequality, BP.IC

Abstract

The theory of interpolation of Banach spaces arose from the need to prove the continuity of certain operators defined on $L_p$ spaces, being generalized to the study of operators in Banach spaces in general. An interpolation scale between $X_0$ and $X_1$ can be seen as a deformation of the space $X_0$ to the space $X_1$, and the intermediate spaces have properties that, in general, merge the properties of $X_0$ and $X_1$. Furthermore, it is common for interpolation methods to generate a twisted sum of the interpolation space through the derivation process. This project aims to study applications of the theory of interpolation to the geometry of Banach spaces, through the study of derived spaces, commutator estimates, and interpolation and derivation of concrete spaces. (AU)