Lower and upper 2-estimates for order bounded sequences and Dunford-Pettis operators between certain classes of Banach lattices
We introduce the class of weak Schur spaces, i.e., Banach lattices in which relatively weakly compact sets and almost order bounded sets coincide. There follows a detailed study of Banach lattices in which every semi-normalized, order bounded, weakly null sequence contains a subsequence satisfying a lower, resp. an upper, 2-estimate. From the previous results we obtain conditions under which non-Dunford-Pettis operators between certain classes of Banach lattices fix a copy of ℓ2.
KeywordsBanach Lattice Order Interval Orlicz Function Null Sequence Unit Vector Basis
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