Speaker: M.Ángeles Japón
Abstract: At first glance, geometry in Banach spaces and metric fixed-point theory seem to be independent areas of research. The goal of this lecture is to expose how these two fields are intrinsically connected. Starting with fixed-point characterizations of weak compactness in different classes of Banach spaces according to their underlying geometry, we will exhibit as particular cases how reflexivity and super-reflexivity can be determined by fixed-point theorems. Finally, we will display some open problems, in particular, whether it is possible to characterize the compact sets $K$ for which the unit ball of \(C(K)\) has the fixed-point property. The Stone-Cech compactification for the positive integers \(\beta\mathbb{N}\) will be our model to claim our conjecture.
