| Title:
|
Remarks on some properties in the geometric theory of Banach spaces (English) |
| Author:
|
El-Sayed, Wagdy Gomaa |
| Author:
|
Fraczek, Krzysztof |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
1 |
| Year:
|
1996 |
| Pages:
|
17-22 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to derive some relationships between the concepts of the property of strong $(\alpha ')$ introduced recently by Hong-Kun Xu and the so-called characteristic of near convexity defined by Goebel and S\c ekowski. Particularly we provide very simple proof of a result obtained by Hong-Kun Xu. (English) |
| Keyword:
|
measure of noncompactness |
| Keyword:
|
near convexity |
| Keyword:
|
the property of strong $(\alpha ')$ |
| MSC:
|
46B20 |
| MSC:
|
47H09 |
| idZBL:
|
Zbl 0852.47025 |
| idMR:
|
MR1396159 |
| . |
| Date available:
|
2009-01-08T18:22:00Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118811 |
| . |
| Reference:
|
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| Reference:
|
[2] Banaś J.: Compactness conditions in the geometric theory of Banach spaces.Nonlinear Analysis T.M.A. 16 (1991), 669-682. MR 1097324 |
| Reference:
|
[3] Banaś J., Frączek K.: Conditions involving compactness in geometry of Banach spaces.Nonlinear T.M.A. 20 (1993), 1217-1230. MR 1219238 |
| Reference:
|
[4] Banaś J., Goebel K.: Measures of Noncompactness in Banach Spaces.Lecture Notes in Pure and Applied Math., vol. 60, M. Dekker, New York, Basel, 1980. MR 0591679 |
| Reference:
|
[5] Daneš J.: A geometric theorem useful in nonlinear analysis.Boll. Un. Mat. Ital. 6 (1972), 369-372. MR 0317130 |
| Reference:
|
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| Reference:
|
[7] Garcia-Falset J., Jimenez-Melado A., Llorens-Fuster E.: A characterization of normal structure in Banach spaces.Fixed Point Theory and Applications (K.K. Tan, ed.), World Scientific, Singapore, 1992, pp. 122-129. |
| Reference:
|
[8] Goebel K., Sȩkowski T.: The modulus of noncompact convexity.Ann. Univ. Mariae Curie- Skłodowska, Sect. A 38 (1984), 41-48. MR 0856623 |
| Reference:
|
[9] Hong-Kun Xu: Measures of noncompactness and normal type structures in Banach spaces.Panamer. Math. J. 3 (1993), 17-34. Zbl 0846.46008, MR 1216273 |
| Reference:
|
[10] Köthe G.: Topological Vector Spaces I.Springer Veralg, Berlin, 1969. MR 0248498 |
| Reference:
|
[11] Lindenstrauss J., Tzafiri L.: Classical Banach Spaces.Springer Verlag, Berlin, 1973. MR 0415253 |
| Reference:
|
[12] Montesinos V.: Drop property equals reflexivity.Studia Math. 87 (1987), 93-110. Zbl 0652.46009, MR 0924764 |
| Reference:
|
[13] Rolewicz S.: On drop property.Studia Math. 85 (1987), 27-35. MR 0879413 |
| . |
