|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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