# 25 mars 2020: 1 événement

### Mercredi 25 mars 13:45-14:45 - Trond Abrahamsen - Université d'Agder

Almost square Banach spaces and relatives

Résumé : Let $X$ be a Banach space with unit sphere $S_X$. We say that $X$ is

• (a) almost square (ASQ) if for all $(x_i)^k_1 \subset S_X$ there exists a sequence $(y_n) \subset S_X$ such that for all $i = 1, . . . , k$ we have $\|x_i \pm y_n\| \to 1$,
• (b) weakly almost square (WASQ) if for all $x \in S_X$ there exists a sequence $(yn) \subset S_X$ weakly convergent to 0 such that $\|x \pm y_n\| \to 1$,
• (c) locally almost square (LASQ) if for all $x \in S_X$ there exists a sequence $(y_n) \subset S_X$ such that $\|x \pm y_n\| \to 1$.

We will provide numerous examples of spaces of types (a) - (c), point out relations between (a) - (c) and diameter properties, and mention some open problems in this regard. Finally we will discuss some old and new results in the isomorphic direction about ASQ spaces.

Lieu : 316Bbis

En savoir plus : Séminaire d’Analyse Fonctionnelle