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 spaces appear as principal ideals of separable Banach lattices. Among other things, it is shown that every such compactum 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 . Some natural questions about this class are left open.
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