| Title:
|
A note on lattice renormings (English) |
| Author:
|
Fabian, Marián |
| Author:
|
Hájek, Petr |
| Author:
|
Zizler, Václav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
263-272 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that every strongly lattice norm on $c_0(\Gamma)$ can be approximated by $C^\infty$ smooth norms. We also show that there is no lattice and G\^ateaux differentiable norm on $C_0[0,\omega_1]$. (English) |
| Keyword:
|
smooth norms |
| Keyword:
|
approximation |
| Keyword:
|
lattice norms |
| Keyword:
|
$c_0(\Gamma)$ |
| Keyword:
|
$C_0[0, \omega_1]$ |
| MSC:
|
46B03 |
| MSC:
|
46B20 |
| MSC:
|
46B26 |
| idZBL:
|
Zbl 0886.46006 |
| idMR:
|
MR1455493 |
| . |
| Date available:
|
2009-01-08T18:30:42Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118924 |
| . |
| Reference:
|
[1] Deville R., Fonf V., Hájek P.: Analytic and polyhedral approximations of convex bodies in separable polyhedral Banach spaces.Israel J. Math., to appear. MR 1639743 |
| Reference:
|
[2] Deville R., Fonf V., Hájek P.: Analytic and $C^k$-smooth approximations of norms in separable Banach spaces.Studia Math., to appear. MR 1398174 |
| Reference:
|
[3] Deville R., Godefroy G., Zizler V.: Smoothness and renormings in Banach spaces.Pitman Monographs and Surveys in Pure and Applied Mathematics 64, 1993. Zbl 0782.46019, MR 1211634 |
| Reference:
|
[4] Dugundji J.: Topology.Allyn and Bacon Inc., 1966. Zbl 0397.54003, MR 0193606 |
| Reference:
|
[5] Haydon R.: Normes infiniment differentiables sur certains espaces de Banach.C.R. Acad. Sci. Paris, t. 315, Serie I (1992), 1175-1178. Zbl 0788.46008, MR 1194512 |
| Reference:
|
[6] Haydon R.: Trees in renormings theory.to appear. MR 1674838 |
| . |
