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Classification problems on Twisted Hilbert spaces

Grant number: 19/23669-0
Support type:Scholarships abroad - Research
Effective date (Start): February 01, 2020
Effective date (End): January 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Wilson Albeiro Cuellar Carrera
Grantee:Wilson Albeiro Cuellar Carrera
Host: Jesus Maria Fernandez Castillo
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Research place: 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.