Classification problems on twisted Hilbert spaces

• Grant number: 19/23669-0
• Support Opportunities: Scholarships abroad - Research
• Start date: February 01, 2020
• End date: January 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Wilson Albeiro Cuellar Carrera
• Grantee: Wilson Albeiro Cuellar Carrera
• Host Investigator: Jesús María Fernández Castillo
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Universidad de Extremadura, Badajoz (UEx), Spain

Abstract

In this project, we study problems in homological theory of Banach spaces. A twisted sum of Hilbert spaces is a Banach X space that contains an isomorphic subspace Y such that both Y and X/Y are isomorphic to Hilbert spaces. This family of spaces has been relevant in the geometry of Banach spaces related to operator extension problems, complemented subspaces, complex interpolation, nonlinear analysis. Our goal is to obtain results in the direction of a classification of twisted Hilbert spaces, studying their general properties and construction of new examples. We are primarily concerned with the properties of being isomorphic to its dual, its square, and its hyperplanes; approximation property; symplectic structure; ergodicity. The project will be developed at the University of Extremadura with researchers of recognized scientific trajectory in the area. We can name the professors J. M. F. Castillo, F. Cabello Sánchez, J. Suárez de la Fuente and Y. Moreno, among others. (AU)