A Separable Universal Homogeneous Banach Lattice

2020/08/15 by Mary Angelica Tursi, Tursi, Mary Angelica
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2008.06658

openalex publication_date 2020/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of a separable approximately ultra-homogeneous Banach lattice \mathfrakBL 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 Fraïssé class. Some additional results about the structural properties of \mathfrak BL are also proven.

Related

• Amalgamation and injectivity in Banach lattices
• Disjointly homogeneous Banach lattices and applications
• Almost Fraïssé Banach spaces
• Embeddability, representability and universality involving Banach spaces
• An isometrically universal Banach space induced by a non-universal Boolean algebra