Complexity of weakly null sequences

Dale E. Alspach ; Spiros Argyros

GDML_Books, (1992), p.

Résumé

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 $(x^α_n)_n$ in $C(ω^{ω^{α}})$ 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 Lavrent’ev index of a Baire-1 function and use the index to sharpen some results of Alspach and Odell on averaging weakly null sequences.

CONTENTS0. Introduction.................................................................................................51. Preliminaries...............................................................................................62. Weakly null sequences and the l¹-index......................................................93. Comparison with the l¹-index.....................................................................124. Construction of weakly null sequences with large oscillation index............215. Reflexive spaces with large oscillation index.............................................336. Comparison with the averaging index........................................................37References....................................................................................................43

1991 Mathematics Subject Classification: Primary 46B20.

Détail

Zbl 0787.46009

EUDML-ID : urn:eudml:doc:219311