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Unconditional structures of weakly null sequences

S. A. Argyros·I. Gasparis
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Abstract

The following dichotomy is established for a normalized weakly null sequence in a Banach space: Either every subsequence admits a convex block subsequence equivalent to the unit vector basis of c, the Banach space of null sequences under the supremum norm, or there exists a subsequence which is boundedly convexly complete. This result generalizes J. Elton's dichotomy on weakly null sequences.

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S. A. Argyros, I. Gasparis. 1999-11-03. Unconditional structures of weakly null sequences. https://arxiv.org/abs/math/9911019

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