Geodesic
Asplund Space: Another Criterion
Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 118-124

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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 $RN$ property). The theorem is formulated in terms of the existence of a supersequentially compact set in $(B(X^{**}),\omega^*)$, where $B(X^{**})$ stands for the unit ball of the second dual of $X$ and $\omega^*$ 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.
Keywords: Asplund space, supersequentially compact set, Radon–Nikodým property, Bochner integral, Banach space. 
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     author = {V. I. Rybakov},
     title = {Asplund {Space:} {Another} {Criterion}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a12/}
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V. I. Rybakov. Asplund Space: Another Criterion. Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 118-124. http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a12/