The strong Nakano property in Banach lattices

2024/01/28 by Youssef Azouzi, Azouzi, Youssef, Asma Ben Rjeb +3 · 1 citation
Mathematics · #46B42 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2401.15629

openalex publication_date 2024/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the strong Nakano property in Banach lattices with a special focus on free Banach lattices. We show that for every finite dimensional Banach space E, the free Banach lattice FBL[E] has the strong Nakano property with a constant independent of the dimension. It is also shown that if FBL[E] has the strong Nakano property, then E cannot contain subspaces isomorphic to neither c₀ nor L₁.

Cited by

• Order denseness in free Banach lattices

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• The free Banach lattice generated by a Banach space
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