Abstract
The theorem proved in this paper establishes conditions under which a Banach space X is an Asplund space (i.e., its dual space is a space with the Radon-Nikodym (RN) property). The theorem is formulated in terms of the existence of a supersequentially compact set in (B(X **), ω *), where B(X **) stands for the unit ball of the second dual of X and ω* for the weak topology on the ball. The example presented in the paper shows that one cannot get rid of some restrictive conditions in the theorem in general.
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Rybakov, V.I. Asplund space: Another criterion. Math Notes 82, 104–109 (2007). https://doi.org/10.1134/S0001434607070139
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DOI: https://doi.org/10.1134/S0001434607070139