Free dual spaces and free Banach lattices

2022/10/17 by Enrique García-Sánchez, García-Sánchez, Enrique, Pedro Tradacete +1 · 1 citation
Mathematics · #46A11 #46B10 #46B42 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2210.09225

openalex publication_date 2022/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The relation between the free Banach lattice generated by a Banach space and free dual spaces is clarified. In particular, it is shown that for every Banach space E the free p-convex Banach lattice generated by E^**, denoted FBL^p[E^**], admits a canonical isometric lattice embedding into FBL^p[E]^** and FBL^p[E^**] is lattice finitely representable in FBL^p[E]. Moreover, we also show that for p>1, FBL^p[E]^** can actually be considered as the free dual p-convex Banach lattice generated by E, whereas for p=1 this happens precisely when E does not contain complemented copies of ℓ₁.

Cited by

• Compact positive multilinear operators on Banach lattices

Related

• Free Banach lattices
• Free quasi-Banach lattices
• Free Banach lattices over pre-ordered Banach spaces
• Lattice embeddings in free Banach lattices over lattices
• Free Banach lattices generated by a lattice and projectivity