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RNP and KMP are equivalent for some Banach spaces with shrinking basis. (English) Zbl 0854.46016
Summary: We get a characterization of PCP in Banach spaces with shrinking basis. Also, we prove that the Radon-Nikodym and Krein-Milman properties are equivalent for closed, convex and bounded subsets of some Banach spaces with shrinking basis.

MSC:
46B22 Radon-Nikodým, Kreĭn-Milman and related properties
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46B20 Geometry and structure of normed linear spaces
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