| Title:
|
On uniformly Gâteaux smooth $C^{(n)}$-smooth norms on separable Banach spaces (English) |
| Author:
|
Fabian, Marián |
| Author:
|
Zizler, Václav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
657-672 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Every separable Banach space with $C^{(n)}$-smooth norm (Lipschitz bump function) admits an equivalent norm (a Lipschitz bump function) which is both uniformly Gâteaux smooth and $C^{(n)}$-smooth. If a Banach space admits a uniformly Gâteaux smooth bump function, then it admits an equivalent uniformly Gâteaux smooth norm. (English) |
| MSC:
|
46B03 |
| MSC:
|
46B20 |
| idZBL:
|
Zbl 1011.46010 |
| idMR:
|
MR1708330 |
| . |
| Date available:
|
2009-09-24T10:26:17Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127517 |
| . |
| Reference:
|
[BF] J.M. Borwein, M. Fabian: On convex functions having points of Gâteaux differentiability which are not points of Fréchet differentiability.Canadian J. Math. 45 (1993), 1121–1134. MR 1247537, 10.4153/CJM-1993-062-8 |
| Reference:
|
[C] H. Cartan: Calcul différentiel formes différentielles.Herman, Paris 1967. MR 0223194 |
| Reference:
|
[DGZ] R. Deville, G. Godefroy, V. Zizler: Smoothness and renormings in Banach spaces.Pitman Monographs, No. 64, Longman House, Harlow, 1993. MR 1211634 |
| Reference:
|
[FWZ] M. Fabian, J.H.M. Whitfield, V. Zizler: Norms with locally Lipschitzian derivatives.Israel J. Math. 44 (1983), 262–276. MR 0693663, 10.1007/BF02760975 |
| Reference:
|
[MV] D.P. McLaughlin, J.D. Vanderwerff: Higher oreder Gâteaux smooth bump functions on Banach spaces.Bull. Australian Math. Soc. 51 (1995), 291–300. MR 1322795, 10.1017/S000497270001412X |
| Reference:
|
[P] R.R. Phelps: Convex functions, monotone operators and differentiability.Lecture Notes in Math. No. 1364, Springer Verlag, 1993. Zbl 0921.46039, MR 1238715 |
| Reference:
|
[T] W.K. Tang: Uniformly differentiable bump functions.Preprint. Zbl 0876.46007, MR 1421846 |
| . |
