Operators on C(ω^α) which do not preserve C(ω^α)

Alspach, Dale. "Operators on C(ω^α) which do not preserve C(ω^α)." Fundamenta Mathematicae 153.1 (1997): 81-98. <http://eudml.org/doc/212216>.

@article{Alspach1997,
abstract = {It is shown that if α,ζ are ordinals such that 1 ≤ ζ < α < ζω, then there is an operator from $C(ω^\{ω^α\})$ onto itself such that if Y is a subspace of $C(ω^\{ω^α\})$ which is isomorphic to $C(ω^\{ω^α\})$, then the operator is not an isomorphism on Y. This contrasts with a result of J. Bourgain that implies that there are uncountably many ordinals α for which for any operator from $C(ω^\{ω^α\})$ onto itself there is a subspace of $C(ω^\{ω^α\})$ which is isomorphic to $C(ω^\{ω^α\})$ on which the operator is an isomorphism.},
author = {Alspach, Dale},
journal = {Fundamenta Mathematicae},
keywords = {ordinal index; Szlenk index; Banach space of continuous functions},
language = {eng},
number = {1},
pages = {81-98},
title = {Operators on C(ω^α) which do not preserve C(ω^α)},
url = {http://eudml.org/doc/212216},
volume = {153},
year = {1997},
}

TY - JOUR
AU - Alspach, Dale
TI - Operators on C(ω^α) which do not preserve C(ω^α)
JO - Fundamenta Mathematicae
PY - 1997
VL - 153
IS - 1
SP - 81
EP - 98
AB - It is shown that if α,ζ are ordinals such that 1 ≤ ζ < α < ζω, then there is an operator from $C(ω^{ω^α})$ onto itself such that if Y is a subspace of $C(ω^{ω^α})$ which is isomorphic to $C(ω^{ω^α})$, then the operator is not an isomorphism on Y. This contrasts with a result of J. Bourgain that implies that there are uncountably many ordinals α for which for any operator from $C(ω^{ω^α})$ onto itself there is a subspace of $C(ω^{ω^α})$ which is isomorphic to $C(ω^{ω^α})$ on which the operator is an isomorphism.
LA - eng
KW - ordinal index; Szlenk index; Banach space of continuous functions
UR - http://eudml.org/doc/212216
ER -