Authors: Lopez-Abad, Jorge
Todorčević, Stevo 
Title: Pre-compact families of finite sets of integers and weakly null sequences in Banach spaces
Journal: Topology and its Applications
Volume: 156
Issue: 7
First page: 1396
Last page: 1411
Issue Date: 1-Apr-2009
Rank: M23
ISSN: 0166-8641
DOI: 10.1016/j.topol.2008.12.026
Abstract: 
In this paper we use the Nash-Williams theory of fronts and barriers to study weakly null sequences in Banach spaces. Specifically, we show how barriers relate to the classical fact that C (K) with K a countable compactum is c0-saturated. Another result relates the notion of a barrier to the Maurey-Rosenthal example of a weakly null sequence with no unconditional subsequences. In particular, we construct examples of weakly-null sequences which are α-unconditional but not β-unconditional.
Keywords: Barrier | c -saturation 0 | Unconditionality
Publisher: Elsevier

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