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arXiv · 2208.03065

Compact spaces associated to separable Banach lattices

Antonio Avilés·Gonzalo Martínez Cervantes·Abraham Rueda Zoca·Pedro Tradacete
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Abstract

We study the class of compact spaces that appear as structure spaces of separable Banach lattices. In other words, we analyze what $C(K)$ spaces appear as principal ideals of separable Banach lattices. Among other things, it is shown that every such compactum $K$ admits a strictly positive regular Borel measure of countable type that is analytic, and in the nonmetrizable case these compacta are saturated with copies of $\beta\mathbb N$. Some natural questions about this class are left open.

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Antonio Avilés, Gonzalo Martínez Cervantes, Abraham Rueda Zoca, Pedro Tradacete. 2022-08-05. Compact spaces associated to separable Banach lattices. https://arxiv.org/abs/2208.03065

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