Weakly null sequences in the Banach space C(K)

Gasparis, I.; Odell, E.; Wahl, B.

Weakly null sequences in the Banach space C(K)

Authors

Gasparis, I.

Odell, E.

Wahl, B.

Description

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.
36 pages