A remark on localized weak precompactness in Banach spaces
Matsuda, Minoru
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 271-276 / Harvested from Czech Digital Mathematics Library
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We give a characterization of $K$-weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.

Publié le : 1999-01-01
Classification:  46B07,  46B20,  46B22,  46B50,  46G05,  49J50 
@article{119082,
     author = {Minoru Matsuda},
     title = {A remark on localized weak precompactness in Banach spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {271-276},
     zbl = {0983.46011},
     mrnumber = {1732647},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119082}
}

Matsuda, Minoru. A remark on localized weak precompactness in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 271-276. http://gdmltest.u-ga.fr/item/119082/

Bator E.M.; Lewis P.W. Weak precompactness and the weak RNP, Bull. Polish Acad. Sci. Math. 37 (1989), 443-452. (1989) | MR 1101905 | Zbl 0767.46011

Fitzpatrick S.P. Separably related sets and the Radon-Nikodym property, Illinois J. Math. 29 (1985), 229-247. (1985) | MR 0784521 | Zbl 0546.46009

Matsuda M. A characterization of Pettis sets in terms of the Bourgain property, Math. Japon. 41 (1995), 433-439. (1995) | MR 1326976 | Zbl 0842.46012

Matsuda M. On localized weak precompactness in Banach spaces, Publ. RIMS, Kyoto Univ. 32 (1996), 473-491. (1996) | MR 1409798 | Zbl 0863.46010

Rosenthal H. A characterization of Banach spaces containing $l_1$, Proc. Nat. Acad. Sci. 71 (1974), 2411-2413. (1974) | MR 0358307 | Zbl 0297.46013