Unconditional structures of weakly null sequences

@article{Argyros1999UnconditionalSO,
  title={Unconditional structures of weakly null sequences},
  author={Spiros A. Argyros and Ioannis Gasparis},
  journal={Transactions of the American Mathematical Society},
  year={1999},
  volume={353},
  pages={2019-2058}
}
  • S. Argyros, I. Gasparis
  • Published 3 November 1999
  • Mathematics
  • Transactions of the American Mathematical Society
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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