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arXiv · 2508.11648

Order denseness in free Banach lattices

Youssef Azouzi·Wassim Dhifaoui
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Abstract

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 $FBL^{(p)}[E],~~1 ^leq p \leq \infty,$ 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.

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Youssef Azouzi, Wassim Dhifaoui. 2025-08-02. Order denseness in free Banach lattices. https://arxiv.org/abs/2508.11648

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