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arXiv · 2609.06689

Order closure, order adherence and Fatou norms

A. Avilés·M. A. Taylor·P. Tradacete
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Abstract

We record two results in the theory of vector and Banach lattices related to order adherence. First, we give a negative answer to Gao and Leung's question on whether the $uo$-adherence of sublattices must be order closed. Second, we present a self-contained counterexample showing that a Banach lattice with a weakly Fatou norm need not admit any equivalent lattice norm with the Fatou property.

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A. Avilés, M. A. Taylor, P. Tradacete. 2026-09-06. Order closure, order adherence and Fatou norms. https://arxiv.org/abs/2609.06689

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