Complexity of weakly null sequences

@book{DaleE1992,
abstract = {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....................................................................................................431991 Mathematics Subject Classification: Primary 46B20.},
author = {Dale E. Alspach, Spiros Argyros},
keywords = {ordinal index; complexity; unconditional; L₁-predual; C(K) space; oscillatory behavior of pointwise converging sequences; oscillation of sequences; sequences of indicator functions; oscillation index; averaging weakly null sequences},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Complexity of weakly null sequences},
url = {http://eudml.org/doc/219311},
year = {1992},
}

TY - BOOK
AU - Dale E. Alspach
AU - Spiros Argyros
TI - Complexity of weakly null sequences
PY - 1992
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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....................................................................................................431991 Mathematics Subject Classification: Primary 46B20.
LA - eng
KW - ordinal index; complexity; unconditional; L₁-predual; C(K) space; oscillatory behavior of pointwise converging sequences; oscillation of sequences; sequences of indicator functions; oscillation index; averaging weakly null sequences
UR - http://eudml.org/doc/219311
ER -