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Pre-compact families of finite sets of integers and weakly null sequences in Banach spaces |
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| Authors: | J. Lopez-Abad S. Todorcevic |
| Affiliation: | a Equipe de Logique Mathématique, Université Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France b C.N.R.S., U.M.R. 7056 et Université Paris 7, U.F.R. de Mathématiques, Case 7012, 2 Place Jussieu, 75251 Paris Cedex 5, France c Department of Mathematics, University of Toronto, Toronto, Canada, M5S 3G3 |
| 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: | primary, 05D10, 46B20, 46A35 secondary, 03E05 |
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