| Title:
|
A remark on localized weak precompactness in Banach spaces (English) |
| Author:
|
Matsuda, Minoru |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
271-276 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a characterization of $K$-weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions. (English) |
| Keyword:
|
$K$-weakly precompact set |
| Keyword:
|
uniform Gateaux differentiability |
| MSC:
|
46B07 |
| MSC:
|
46B20 |
| MSC:
|
46B22 |
| MSC:
|
46B50 |
| MSC:
|
46G05 |
| MSC:
|
49J50 |
| idZBL:
|
Zbl 0983.46011 |
| idMR:
|
MR1732647 |
| . |
| Date available:
|
2009-01-08T18:51:56Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119082 |
| . |
| Reference:
|
[1] Bator E.M., Lewis P.W.: Weak precompactness and the weak RNP.Bull. Polish Acad. Sci. Math. 37 (1989), 443-452. Zbl 0767.46011, MR 1101905 |
| Reference:
|
[2] Fitzpatrick S.P.: Separably related sets and the Radon-Nikodym property.Illinois J. Math. 29 (1985), 229-247. Zbl 0546.46009, MR 0784521 |
| Reference:
|
[3] Matsuda M.: A characterization of Pettis sets in terms of the Bourgain property.Math. Japon. 41 (1995), 433-439. Zbl 0842.46012, MR 1326976 |
| Reference:
|
[4] Matsuda M.: On localized weak precompactness in Banach spaces.Publ. RIMS, Kyoto Univ. 32 (1996), 473-491. Zbl 0863.46010, MR 1409798 |
| Reference:
|
[5] Rosenthal H.: A characterization of Banach spaces containing $l_1$.Proc. Nat. Acad. Sci. 71 (1974), 2411-2413. Zbl 0297.46013, MR 0358307 |
| . |
