Semilattice Structures of Spreading Models
Functional Analysis
2007-08-24 v1
Abstract
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.
Cite
@article{arxiv.0708.3126,
title = {Semilattice Structures of Spreading Models},
author = {Denny H. Leung and Wee-Kee Tang},
journal= {arXiv preprint arXiv:0708.3126},
year = {2007}
}