A Separable Universal Homogeneous Banach Lattice

Abstract

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