| Title:
|
Deformation of Banach spaces (English) |
| Author:
|
Banaś, Józef |
| Author:
|
Fraczek, Krzysztof |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
47-53 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using some moduli of convexity and smoothness we introduce a function which allows us to measure the deformation of Banach spaces. A few properties of this function are derived and its applicability in the geometric theory of Banach spaces is indicated. (English) |
| Keyword:
|
uniformly convex Banach space |
| Keyword:
|
uniformly smooth Banach space |
| Keyword:
|
modulus of convexity |
| Keyword:
|
modulus of smoothness |
| MSC:
|
46B20 |
| idZBL:
|
Zbl 0817.46016 |
| idMR:
|
MR1240202 |
| . |
| Date available:
|
2009-01-08T18:00:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118554 |
| . |
| Reference:
|
[1] Alonso J., Ullan A.: Moduli of convexity.Functional Analysis and Approximation, edited by P.L. Papini, Bagni di Lucca, Italy, May 16-20, 1988, 25-33. MR 1001569 |
| Reference:
|
[2] Banaś J.: On moduli of smoothness of Banach spaces.Bull. Pol. Acad. Sci. Math. 34 (1986), 287-293. MR 0874871 |
| Reference:
|
[3] Banaś J., Hajnosz A., Wȩdrychowicz S.: On convexity and smoothness of Banach space.Comment. Math. Univ. Carolinae 31 (1990), 445-452. MR 1078479 |
| Reference:
|
[4] Clarkson J.A.: Uniformly convex spaces.Trans. Amer. Math. Soc. 40 (1936), 396-414. Zbl 0015.35604, MR 1501880 |
| Reference:
|
[5] Daneš J.: On local and global moduli of convexity.Comment. Math. Univ. Carolinae 17 (1976), 413-420. MR 0417755 |
| Reference:
|
[6] Day M.M.: Uniform convexity in factor and conjugate spaces.Ann. of Math. 45 (1944), 375-385. Zbl 0063.01058, MR 0010779 |
| Reference:
|
[7] Goebel K., Kirk W.A.: Topics in Metric Fixed Point Theory.Cambridge University Press, 1991. MR 1074005 |
| Reference:
|
[8] Gurarii V.I.: Differential properties of the convexity moduli of Banach spaces (in Russian).Mat. Issled. 2 (1967), 141-148. MR 0211245 |
| Reference:
|
[9] Hanner O.: On the uniform convexity of $L^p$ and $l^p$.Arkiv Mat. 3 (1956), 239-244. MR 0077087 |
| Reference:
|
[10] Liokoumovich V.I.: The existence of $B$-spaces with non-convex modulus of convexity (in Russian).Izv. Vyss. Uchebn. Zaved. Matematica 12 (1973), 43-50. |
| Reference:
|
[11] Milman V.D.: The geometric theory of Banach spaces.Part II, Uspehi Mat. Nauk 26 (1971), 73-149. MR 0420226 |
| Reference:
|
[12] Nordlander G.: The modulus of convexity in normed spaces.Arkiv Mat. 4 (1960), 15-17. MR 0140915 |
| Reference:
|
[13] Ullan A.: Modulos de convexidad y lisura en espacios normados.Univ. de Extremadura, Spain, 1991. MR 1174971 |
| . |
