Geodesic
A remark on localized weak precompactness in Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 271-276.

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We give a characterization of $K$-weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.
Classification : 46B07, 46B20, 46B22, 46B50, 46G05, 49J50
Keywords: $K$-weakly precompact set; uniform Gateaux differentiability 
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Matsuda, Minoru. A remark on localized weak precompactness in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 271-276. http://geodesic.mathdoc.fr/item/CMUC_1999__40_2_a7/