Banach Lattices with the Subsequence Splitting Property
Lutz W. Weis · Proceedings of the American Mathematical Society · 1989
A Banach lattice $X$ has SSP if every bounded sequence in $X$ has a subsequence that splits into a $X$-equi-integrable sequence and a sequence with pairwise disjoint support. We characterize such lattices in terms of uniform order continuity conditions and ultrapowers. This implies that rearrangement invariant function spaces with the Fatou-property have SSP.