ar X iv : m at h / 92 02 20 4 v 1 [ m at h . FA ] 2 8 Fe b 19 92 COMPLEXITY OF WEAKLY NULL SEQUENCES
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چکیده
We introduce an ordinal index which measures the complexity of a weakly null sequence, and show that a construction due to J. Schreier can be iterated to produce for each α < ω1, a weakly null sequence (xαn)n in C ( ωω α ) with complexity α. As in the Schreier example each of these is a sequence of indicator functions which is a suppression-1 unconditional basic sequence. These sequences are used to construct Tsirelson-like spaces of large index. We also show that this new ordinal index is related to the Lavrentiev index of a Baire-1 function and use the index to sharpen some results of Alspach and Odell on averaging weakly null sequences.
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