Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591793 | Journal of Functional Analysis | 2007 | 10 Pages |
Abstract
It is proved that every non-trivial weak-Cauchy sequence in a Banach space with the PCP (the Point of Continuity Property) has a boundedly complete basic subsequence. The following result, due independently to S. Bellenot and C. Finet, is then deduced as a corollary. If a Banach space X has separable dual and the PCP, then every non-trivial weak-Cauchy sequence in X has a subsequence spanning an order-one quasi-reflexive space.
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