This is an announcement for the paper "Weakly null sequences in the Banach space C(K)" by I. Gasparis, E. Odell, and B. Wahl.

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.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B03

Remarks: 36 pages

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Submitted from: combs@mail.ma.utexas.edu

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