On the structure of non dentable subsets of C(ω^ωk)

2011/03/02 by Pericles D Pavlakos, Pavlakos, Pericles D, Minos Petrakis +1
Computer Science · Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA

paper · pdf · doi:10.48550/arxiv.1103.0366

18 pages,accepted in Studia Mathematica

arxiv created 2011/03/02 · openalex publication_date 2011/03/02 · arxiv updated 2011/03/03 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

It is shown that there is no K closed convex bounded non-dentable subset of C(ω^{ω k}) such that on the subsets of K the PCP and the RNP are equivalent properties. Then applying Schachermayer-Rosenthal theorem, we conclude that every non-dentable K contains non-dentable subset L so that on L the weak topology coincides with the norm one. It follows from known results that the RNP and the KMP are equivalent properties on the subsets of C(ω^{ω k}).

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