Semilattice structures of spreading models

Abstract

Given a Banach space X,denote by SPω (X) the set of equivalence classes of spreading models of X generated by normalized weakly null sequences in X .It is known that SPω (X) is a semilattice, i.e., it is a partially ordered set in which every pair of elements has a least upper bound. We show that every countable semilattice that does not contain an infinite increasing sequence is order isomorphic to SPω (X) for some separable Banach space X. © 2008 American Mathematical Society.