Komlos Properties in Banach Lattices
Several Komlós like properties in Banach lattices are investigated. We prove that $C(K)$ fails the $oo$-pre-Komlós property, assuming that the compact Hausdorff space $K$ has a nonempty separable open subset $U$ without isolated points such that every $u\in U$ has countable neighborhood base. We prove also that for any infinite dimensional Banach lattice $E$ there is an unbounded convex $uo$-pre-Komlós set $C\subseteq E_+$ which is not $uo$-Komlós.
math.FA↗