Dándole una vuelta a las rotaciones de Mazur

Start: 2 June 2025 09:00
End: 2 June 2025 09:00
Categories: Conference , Seminar , Instituto de Matemáticas UGR

Where: Seminario Departamento Analisis Matematico, Facultad de Ciencias

IMAG Functional Analysis Seminar
Title: Dándole una vuelta a las rotaciones de Mazur
By Javier Cabello (Universidad de Extremadura)
Abstract: Let $H$ be a Hilbert space. It is quite clear that its sphere, say $S\subset H$, fulfills that for each $x,y\in S$ there exists a (linear, onto) isometry $T_{x,y}:H\to H$ such that $T_{x,y}(x)=y$. The Banach spaces that fulfil this are called {\em transitive}. It stands to reason that the only separable, transitive Banach space is the Hilbert space $\ell_2$ (needless to say, unique up to isometries). Well, the famous Mazur rotations Problem is to determine whether this is true or not. Among the several properties related to transitivity, today we will focus on the uniform semi-micro transitivity and how this leads to the study ofconvex bodies in finite dimensional spaces.