Semilattice Structures of Spreading Models

2007/08/23 by Denny H. Leung, Leung, Denny H., Wee-Kee Tang +1
Mathematics · #46B15 #46B20 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B15 #msc:46B20

paper · pdf · doi:10.48550/arxiv.0708.3126

arxiv created 2007/08/23 · arxiv updated 2009/12/01

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.

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