Unconditional structures of weakly null sequences

Argyros, S.; Gasparis, I.

doi:10.1090/S0002-9947-01-02711-8

Unconditional structures of weakly null sequences
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by S. A. Argyros and I. Gasparis PDF

Trans. Amer. Math. Soc. 353 (2001), 2019-2058 Request permission

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 $c_0$, or there exists a subsequence which is boundedly convexly complete.

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