| Title:
|
For a dense set of equivalent norms, a non-reflexive Banach space contains a triangle with no Chebyshev center (English) |
| Author:
|
Veselý, Libor |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
153-158 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a non-reflexive real Banach space. Then for each norm $|\cdot|$ from a dense set of equivalent norms on $X$ (in the metric of uniform convergence on the unit ball of $X$), there exists a three-point set that has no Chebyshev center in $(X,|\cdot|)$. This result strengthens theorems by Davis and Johnson, van Dulst and Singer, and Konyagin. (English) |
| Keyword:
|
renormings |
| Keyword:
|
non-reflexive Banach spaces |
| Keyword:
|
Chebyshev centers |
| MSC:
|
41A65 |
| MSC:
|
46B03 |
| MSC:
|
46B20 |
| idZBL:
|
Zbl 1056.46009 |
| idMR:
|
MR1825379 |
| . |
| Date available:
|
2009-01-08T19:08:54Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119230 |
| . |
| Reference:
|
[DJ] Davis W.J., Johnson W.B.: A renorming of non-reflexive Banach spaces.Israel J. Math. 14 (1973), 353-367. MR 0322481 |
| Reference:
|
[vDS] van Dulst D., Singer I.: On Kadec-Klee norms on Banach spaces.Studia Math. 54 (1976), 205-211. Zbl 0321.46012, MR 0394132 |
| Reference:
|
[Ho] Holmes R.B.: A course in optimization and best approximation.Lecture Notes in Mathematics 257, Springer-Verlag, 1972. MR 0420367 |
| Reference:
|
[Ja] James R.C.: Reflexivity and the supremum of linear functionals.Ann. Math. 66 (1957), 159-169. Zbl 0079.12704, MR 0090019 |
| Reference:
|
[Ko] Konyagin S.V.: A remark on renormings of nonreflexive spaces and the existence of a Chebyshev center.Moscow Univ. Math. Bull. 43 2 (1988), 55-56. MR 0938075 |
| Reference:
|
[Ve] Veselý L.: A geometric proof of a theorem about non-dual renormings.Proc. Amer. Math. Soc. 127 (1999), 2807-2809. MR 1670431 |
| . |
