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arXiv · 2401.15629

The strong Nakano property in Banach lattices

Youssef Azouzi·Asma Ben Rjeb·Pedro Tradacete
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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 $c_0$ nor $L_1$.

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Youssef Azouzi, Asma Ben Rjeb, Pedro Tradacete. 2024-01-28. The strong Nakano property in Banach lattices. https://arxiv.org/abs/2401.15629

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