Banach spaces & Banach lattices Seminar
Order continuity of induced homomorphisms between free Banach lattices
Speaker: Raúl Enrique Pariente Martín (ICMAT)Date: Friday, 30 October 2026 - 11:45-13:15Place: Aula Gris 2, ICMAT
Abstract:
Let \(T\colon F\rightarrow E\) be a bounded operator between Banach spaces, \(1\leq p\leq \infty\) and let \(\overline T\colon FBL{(p)}[F]\rightarrow FBL^{(p)}[E]\) be the lattice homomorphism induced by \(T\) between the corresponding free p-convex Banach lattices generated by \(F\) and \(E\). We show that \(\overline T\) is order continuous if and only if it is either zero or a lattice isomorphic embedding. In addition, we study when \(FBL^{(p)}[E]\) is order-dense or majorizing in \(FBL^{(q)}[E]\).
