Banach spaces & Banach lattices Seminar
Convexity conditions and free objects in quasi-Banach lattices
Speaker: Alberto Salguero (UCM-ICMAT)Date: Thursday, 24 April 2025 - 12:00Place: Aula Gris 1, ICMAT
Abstract:
The theory of quasi-Banach lattices has received much less attention that its locally convex counterpart, and perhaps the most obvious explanation for this is that one can no longer appeal to Hahn-Banach's Theorem. Not everything is lost, however, since there are quite a few techniques that survive the lack of local convexity. Among them, the notions of p-convexification and p-concavification do still work, to some extent. Our aim in this talk is to use them to propose several reasonable notions of “free quasi-Banach lattice” associated to a given quasi-Banach space. Then, we will focus in two simple questions: when do such free objects exist, and what relations can be established between them. In our way, we would like to support the fact that the theory of quasi-Banach lattices may be hard, but it is by no means uninteresting. This is part of a joint work with P. Tradacete and N. Trejo-Arroyo.
