Weakly compactly generated Banach lattices
Volume 234 / 2016
Studia Mathematica 234 (2016), 165-183
MSC: 46B42, 46B50, 46B26.
DOI: 10.4064/sm8513-5-2016
Published online: 15 July 2016
Abstract
We study the different ways in which a weakly compact set can generate a Banach lattice. Among other things, it is shown that in an order continuous Banach lattice $X$, the existence of a weakly compact set $K\subset X$ such that $X$ coincides with the band generated by $K$ implies that $X$ is weakly compactly generated.
