Semilattice Structures of Spreading Models

Details Semilattice Structures of Spreading Models Semilattice Structures of Spreading Models

2007-08-23

arxiv.org/abs/0708.3126v1

Mathematics

Functional Analysis

Scientific paper

Given a Banach space X, denote by SP_{w}(X) the set of equivalence classes of spreading models of X generated by normalized weakly null sequences in X. It is known that SP_{w}(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 SP_{w}(X) for some separable Banach space X.

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