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Complexity of weakly null sequences. (English) Zbl 0787.46009

The main subject of investigation is the oscillatory behavior of pointwise converging sequences. A new ordinal index which measures the oscillation of sequences is introduced. It is proved that this new index is smaller than other known similar ordinal indices. By constructing special examples of sequences of indicator functions in \(C(K)\) it is shown that the oscillation index can be arbitrarily large. The connection with averaging weakly null sequences is considered.

MSC:

46B20 Geometry and structure of normed linear spaces
46B10 Duality and reflexivity in normed linear and Banach spaces
46E15 Banach spaces of continuous, differentiable or analytic functions
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