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The asymptotic-norming and the Radon-Nikodým properties are equivalent in separable Banach spaces

Authors: N. Ghoussoub and B. Maurey
Journal: Proc. Amer. Math. Soc. 94 (1985), 665-671
MSC: Primary 46B20; Secondary 46B22
MathSciNet review: 792280
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Abstract: We show that the asymptotic-norming and the Radon-Nikodym properties are equivalent, settling a problem of James and Ho [9]. In the process, we give a positive solution to two questions of Edgar and Wheeler [6] concerning Cech-complete Banach spaces. We also show that a separable Banach space with the Radon-Nikodym property semi-embeds in a separable dual whenever it has a norming space not containing an isomorphic copy of $ {l_1}$. This gives a partial answer to a problem of Bourgain and Rosenthal [3].

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Keywords: Asymptotic-norming and Radon-Nikodym properties, semi-embeddings
Article copyright: © Copyright 1985 American Mathematical Society