Compact spaces associated to separable Banach lattices

Abraham Rueda Zoca; Antonio Avil\'es; Gonzalo Mart\'inez Cervantes; Pedro Tradacete

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Compact spaces associated to separable Banach lattices

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arxiv 2208.03065 v2 pith:PIFPDV7A submitted 2022-08-05 math.FA math.GN

Compact spaces associated to separable Banach lattices

Antonio Avil\'es , Gonzalo Mart\'inez Cervantes , Abraham Rueda Zoca , Pedro Tradacete This is my paper

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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.

Compact spaces associated to separable Banach lattices

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