2025/08/02 by Youssef Azouzi, Azouzi, Youssef, Wassim Dhifaoui +1
Mathematics · #46B42 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2508.11648
openalex publication_date 2025/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a fundamental property: the free vector lattice FVL[E] over a Banach space E is order dense in the free p-convex Banach lattice FBL(p)[E],~~1 leq p ≤ ∞, if and only if E is finite-dimensional. In a recent work, Oikhberg, Tradacete, Taylor, and Troitsky claimed that order denseness holds for all Banach spaces. We point out a gap in their proof, and consequently, any conclusions relying on this claim require reexamination -- a task we also undertake in this present paper. A key tool in our approach, which also leads to a partial answer to an open question recently posed by these authors.