A Separable Universal Homogeneous Banach Lattice

Abstract

Abstract We prove the existence of a separable approximately ultra-homogeneous Banach lattice $\mathfrak {B}\mathfrak {L}$ that is isometrically universal for separable Banach lattices. This is done by showing that that the class of finitely generated Banach lattices has the Amalgamation Property and thus form a metric Fraïssé class. Some additional results about the structural properties of $\mathfrak { BL}$ are also proven.