Banach spaces & Banach lattices Seminar
Free products of Banach lattices
Speaker: Gonzalo Martínez-Fernández (ICMAT)Date: Wednesday, 25 February 2026 - 12:00Place: Aula Gris 1, ICMAT
Abstract:
Free products provide a universal way of combining a family of Banach lattices into a single one, without imposing relations between them beyond those already present in each factor. They are characterized by a natural extension property for lattice homomorphisms. Using free Banach lattices, this abstract description can be turned into an explicit construction, obtained as a suitable quotient of a free object, making the structure of the free product completely concrete.
A remarkable connection emerges with topology: forming free products of C(K)-spaces corresponds to performing a join at the level of compact spaces. In particular, this connection allows us to detect the anomalous phenomenon of the existence of free factors of free Banach lattices that are not themselves free Banach lattices.
