# Complexity of weakly null sequences

Dale E. Alspach; Spiros Argyros

- Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1992

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topDale E. Alspach, and Spiros Argyros. Complexity of weakly null sequences. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1992. <http://eudml.org/doc/219311>.

@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 -

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