A remark on localized weak precompactness in Banach spaces

Minoru Matsuda

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 2, page 271-276
  • ISSN: 0010-2628

Abstract

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We give a characterization of K -weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.

How to cite

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Matsuda, Minoru. "A remark on localized weak precompactness in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 271-276. <http://eudml.org/doc/248396>.

@article{Matsuda1999,
abstract = {We give a characterization of $K$-weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.},
author = {Matsuda, Minoru},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$K$-weakly precompact set; uniform Gateaux differentiability; -weakly precompact set; directional derivatives space},
language = {eng},
number = {2},
pages = {271-276},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A remark on localized weak precompactness in Banach spaces},
url = {http://eudml.org/doc/248396},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Matsuda, Minoru
TI - A remark on localized weak precompactness in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 2
SP - 271
EP - 276
AB - We give a characterization of $K$-weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.
LA - eng
KW - $K$-weakly precompact set; uniform Gateaux differentiability; -weakly precompact set; directional derivatives space
UR - http://eudml.org/doc/248396
ER -

References

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  1. Bator E.M., Lewis P.W., Weak precompactness and the weak RNP, Bull. Polish Acad. Sci. Math. 37 (1989), 443-452. (1989) Zbl0767.46011MR1101905
  2. Fitzpatrick S.P., Separably related sets and the Radon-Nikodym property, Illinois J. Math. 29 (1985), 229-247. (1985) Zbl0546.46009MR0784521
  3. Matsuda M., A characterization of Pettis sets in terms of the Bourgain property, Math. Japon. 41 (1995), 433-439. (1995) Zbl0842.46012MR1326976
  4. Matsuda M., On localized weak precompactness in Banach spaces, Publ. RIMS, Kyoto Univ. 32 (1996), 473-491. (1996) Zbl0863.46010MR1409798
  5. Rosenthal H., A characterization of Banach spaces containing l 1 , Proc. Nat. Acad. Sci. 71 (1974), 2411-2413. (1974) Zbl0297.46013MR0358307

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