Alspach, Dale E.; Argyros, Spiros Complexity of weakly null sequences. (English) Zbl 0787.46009 Diss. Math. 321, 44 p. (1992). 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. Reviewer: M.I.Kadets (Khar’kov) Cited in 8 ReviewsCited in 62 Documents 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 Keywords:oscillatory behavior of pointwise converging sequences; oscillation of sequences; sequences of indicator functions; oscillation index; averaging weakly null sequences PDFBibTeX XMLCite \textit{D. E. Alspach} and \textit{S. Argyros}, Diss. Math. 321, 44 (1992; Zbl 0787.46009) Full Text: arXiv EuDML