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arXiv · 2604.27841

On the free Banach lattice generated by a lattice

Asma Ben Rjeb·Pedro Tradacete
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Abstract

We study structural properties of the free Banach lattice $FBL\langle L\rangle$ generated by a distributive lattice $L$. We characterize when $FBL\langle L\rangle$ has a strong unit, compute its density character, analyze the density character of order intervals and study when is $FVL\langle L\rangle$ order dense in $FBL\langle L\rangle$. We also study projection bands, quasi-interior points, and Banach lattice homomorphisms induced by lattice homomorphisms. Finally, we show that $FBL\langle L\rangle$ is lattice isometric to $FBL\langle L^{\mathrm{op}}\rangle$, where $L^{\mathrm{op}}$ denotes the opposite lattice.

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Asma Ben Rjeb, Pedro Tradacete. 2026-04-30. On the free Banach lattice generated by a lattice. https://arxiv.org/abs/2604.27841

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