On the structure of non-dentable subsets of $C\left({\omega }^{{\omega }^k}\right)$

@article{PericlesD2011,
abstract = {It is shown that there is no closed convex bounded non-dentable subset K of $C(ω^\{ω^\{k\}\})$ such that on subsets of K the PCP and the RNP are equivalent properties. Then applying the Schachermayer-Rosenthal theorem, we conclude that every non-dentable K contains a non-dentable subset L so that on L the weak topology coincides with the norm topology. It follows from known results that the RNP and the KMP are equivalent on subsets of $C(ω^\{ω^\{k\}\})$.},
author = {Pericles D. Pavlakos, Minos Petrakis},
journal = {Studia Mathematica},
keywords = {Radon-Nikodym property; Krein-Milman property; martingale; operators on ; bush; space with a countable ordinal},
language = {eng},
number = {3},
pages = {205-222},
title = {On the structure of non-dentable subsets of $C(ω^\{ω^\{k\}\})$},
url = {http://eudml.org/doc/285848},
volume = {203},
year = {2011},
}

TY - JOUR
AU - Pericles D. Pavlakos
AU - Minos Petrakis
TI - On the structure of non-dentable subsets of $C(ω^{ω^{k}})$
JO - Studia Mathematica
PY - 2011
VL - 203
IS - 3
SP - 205
EP - 222
AB - It is shown that there is no closed convex bounded non-dentable subset K of $C(ω^{ω^{k}})$ such that on subsets of K the PCP and the RNP are equivalent properties. Then applying the Schachermayer-Rosenthal theorem, we conclude that every non-dentable K contains a non-dentable subset L so that on L the weak topology coincides with the norm topology. It follows from known results that the RNP and the KMP are equivalent on subsets of $C(ω^{ω^{k}})$.
LA - eng
KW - Radon-Nikodym property; Krein-Milman property; martingale; operators on ; bush; space with a countable ordinal
UR - http://eudml.org/doc/285848
ER -