English

Compact spaces associated to separable Banach lattices

Functional Analysis 2023-01-25 v2 General Topology

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)C(K) spaces appear as principal ideals of separable Banach lattices. Among other things, it is shown that every such compactum KK 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 βN\beta\mathbb N. Some natural questions about this class are left open.

Keywords

Cite

@article{arxiv.2208.03065,
  title  = {Compact spaces associated to separable Banach lattices},
  author = {Antonio Avilés and Gonzalo Martínez Cervantes and Abraham Rueda Zoca and Pedro Tradacete},
  journal= {arXiv preprint arXiv:2208.03065},
  year   = {2023}
}

Comments

With respect to previous version: just minor changes to conform to the final published paper

R2 v1 2026-06-25T01:30:14.264Z