| Title:
|
Continuity of the uniform rotundity modulus relative to linear subspaces (English) |
| Author:
|
Fernández, Manuel |
| Author:
|
Palacios, Isidro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
273-277 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the continuity of the rotundity modulus relative to linear subspaces of normed spaces. As a consequence we reduce the study of uniform rotundity relative to linear subspaces to the study of the same property relative to closed linear subspaces of Banach spaces. (English) |
| Keyword:
|
uniform rotundity |
| MSC:
|
46B20 |
| idZBL:
|
Zbl 0886.46013 |
| idMR:
|
MR1455494 |
| . |
| Date available:
|
2009-01-08T18:30:47Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118925 |
| . |
| Reference:
|
[1] Clarkson J.A.: Uniformly convex spaces.Trans. Amer. Math. Soc. 40 (1936), 396-414. Zbl 0015.35604, MR 1501880 |
| Reference:
|
[2] Fakhoury H.: Directions d'uniform convexité dans un space normé.Séminaire Choquet, 14 anné, No. 6 (1974). |
| Reference:
|
[3] Fernández M., Palacios I.: Relative rotundity in $L^p(X)$.Arch. Math. (Basel) 65 (1995), 61-68. MR 1336225 |
| Reference:
|
[4] Fernández M., Palacios I.: Directional uniform rotundity in spaces of essentially bounded vector functions.to appear in Proc. Amer. Math. Soc. MR 1350942 |
| Reference:
|
[5] Garkavi A.L.: The best possible net and the best possible cross-section of a set in a normed space.Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 87-106 Amer. Math. Soc. Transl. Ser. 2 39 (1964), 111-132. MR 0136969 |
| Reference:
|
[6] Goebel K., Kirk W.A.: Topics in Metric Fixed Point Theory.Cambridge Studies in Advanced Mathematics No. 28, Cambridge Univ. Press, Cambridge, MA, 1990. MR 1074005 |
| Reference:
|
[7] Kamińska A., Turett B.: Some remarks on moduli of rotundity in Banach spaces.Acad. Scien. Math. Vol. 36, No. 5-6, 1988. MR 1101665 |
| Reference:
|
[8] Lindenstrauss J., Tzafriri L.: Classical Banach Space II.Springer-Verlag, Berlin-Heidelberg-New York, 1979. MR 0540367 |
| Reference:
|
[9] Ullán A.: Módulos de Convexidad y Lisura en Espacios Normados.Publ. Dep. Matemáticas Univ. Extremadura, No. 27, Badajoz, 1991. MR 1174971 |
| . |
