Séminaires : Séminaire d'Analyse Fonctionnelle

Equipe(s) : af,
Responsables :E. Abakoumov - D. Cordero-Erausquin - G. Godefroy - O. Guédon - B. Maurey - G.Pisier
Email des responsables :
Salle : salle 13 - couloir 15-16 - 4ème étage
Adresse :Campus Pierre et Marie Curie
Description
Le Jeudi à 10h30 -  IMJ-PRG - 4 place Jussieu - 75005 PARIS

Orateur(s) Kasia Wyczesany - Tel Aviv Univ.,
Titre On almost Euclidean and well-complemented subspaces of finite-dimensional normed spaces
Date02/06/2022
Horaire10:30 à 12:00
Diffusion
Résume

In this talk I will discuss a version of an old question of Vitali Milman about almost Euclidean and well-complemented subspaces. In particular, I will introduce a notion of `$\epsilon$-good points', which allows for a convenient reformulation of the problem. Let $(X, \|\cdot\|_X)$ be a normed space. It turns out that if a linear subspace $Y\subset X$ consists entirely of $\epsilon$-good points then the restriction of the norm $\|\cdot \|_X$ to $Y$ must be approximately a multiple of the $\ell_2$ norm and the operator norm of the orthogonal projection onto $Y$ is close to 1. I will present an example of a normed space $X$ of arbitrarily high dimension, whose Banach-Mazur distance from the $\ell_2^{{\rm dim} X}$ is at most $2$, but such that non of its (even two-dimensional) subspaces consists entirely of $\epsilon$-good points. The talk is based on joint work with Timothy Gowers. 

Sallesalle 13 - couloir 15-16 - 4ème étage
AdresseCampus Pierre et Marie Curie
© IMJ-PRG