On the structure of non-dentable subsets of $C(ω^{ω^{k}})$

• Autorzy: Pericles D. Pavlakos , Minos Petrakis
• Języki publikacji: EN

Abstrakty

EN

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 $C(ω^{ω^{k}})$.

Kategorie tematyczne

• 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 203
• Numer: 3
• Strony: 205-222

Daty

wydano

2011

Twórcy

autor

Pericles D. Pavlakos

• Department of Sciences, Section of Mathematics, Technical University of Crete, 73100 Chania, Greece

autor

Minos Petrakis

• Department of Sciences, Section of Mathematics, Technical University of Crete, 73100 Chania, Greece

Identyfikatory

DOI

10.4064/sm203-3-1