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

Ghoussoub, N.; Maurey, B.

doi:10.1090/S0002-9939-1985-0792280-X

The asymptotic-norming and the Radon-Nikodým properties are equivalent in separable Banach spaces
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by N. Ghoussoub and B. Maurey

Proc. Amer. Math. Soc. 94 (1985), 665-671

DOI: https://doi.org/10.1090/S0002-9939-1985-0792280-X

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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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-embeddings in Hilbert space and optimization on

-sets

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