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Weakly null sequences in the Banach space C(K)

I. Gasparis·E. Odell·B. Wahl
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Abstract

The hierarchy of the block bases of transfinite normalized averages of a normalized Schauder basic sequence is introduced and a criterion is given for a normalized weakly null sequence in C(K), the Banach space of scalar valued functions continuous on the compact metric space K, to admit a block basis of normalized averages equivalent to the unit vector basis of c_0, the Banach space of null scalar sequences. As an application of this criterion, it is shown that every normalized weakly null sequence in C(K), for countable K, admits a block basis of normalized averages equivalent to the unit vector basis of c_0.

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I. Gasparis, E. Odell, B. Wahl. 2004-02-12. Weakly null sequences in the Banach space C(K). https://arxiv.org/abs/math/0402202

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