Remarks on some properties in the geometric theory of Banach spaces

Wagdy Gomaa El-Sayed; Krzysztof Fraczek

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 1, page 17-22
  • ISSN: 0010-2628

Abstract

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The aim of this paper is to derive some relationships between the concepts of the property of strong ( α ' ) introduced recently by Hong-Kun Xu and the so-called characteristic of near convexity defined by Goebel and Sȩkowski. Particularly we provide very simple proof of a result obtained by Hong-Kun Xu.

How to cite

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El-Sayed, Wagdy Gomaa, and Fraczek, Krzysztof. "Remarks on some properties in the geometric theory of Banach spaces." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 17-22. <http://eudml.org/doc/247906>.

@article{El1996,
abstract = {The aim of this paper is to derive some relationships between the concepts of the property of strong $(\alpha ^\{\prime \})$ introduced recently by Hong-Kun Xu and the so-called characteristic of near convexity defined by Goebel and Sȩkowski. Particularly we provide very simple proof of a result obtained by Hong-Kun Xu.},
author = {El-Sayed, Wagdy Gomaa, Fraczek, Krzysztof},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {measure of noncompactness; near convexity; the property of strong $(\alpha ^\{\prime \})$; property of strong ; near convexity},
language = {eng},
number = {1},
pages = {17-22},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Remarks on some properties in the geometric theory of Banach spaces},
url = {http://eudml.org/doc/247906},
volume = {37},
year = {1996},
}

TY - JOUR
AU - El-Sayed, Wagdy Gomaa
AU - Fraczek, Krzysztof
TI - Remarks on some properties in the geometric theory of Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 1
SP - 17
EP - 22
AB - The aim of this paper is to derive some relationships between the concepts of the property of strong $(\alpha ^{\prime })$ introduced recently by Hong-Kun Xu and the so-called characteristic of near convexity defined by Goebel and Sȩkowski. Particularly we provide very simple proof of a result obtained by Hong-Kun Xu.
LA - eng
KW - measure of noncompactness; near convexity; the property of strong $(\alpha ^{\prime })$; property of strong ; near convexity
UR - http://eudml.org/doc/247906
ER -

References

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  2. Banaś J., Compactness conditions in the geometric theory of Banach spaces, Nonlinear Analysis T.M.A. 16 (1991), 669-682. (1991) MR1097324
  3. Banaś J., Frączek K., Conditions involving compactness in geometry of Banach spaces, Nonlinear T.M.A. 20 (1993), 1217-1230. (1993) MR1219238
  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. MR0591679
  5. Daneš J., A geometric theorem useful in nonlinear analysis, Boll. Un. Mat. Ital. 6 (1972), 369-372. (1972) MR0317130
  6. Daneš J., On densifying and related mappings and their application in nonlinear functional analysis, Theory of Nonlinear Operators, Akademie-Verlag, Berlin, 1974, pp. 15-56. MR0361946
  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. 
  8. Goebel K., Sȩkowski T., The modulus of noncompact convexity, Ann. Univ. Mariae Curie- Skłodowska, Sect. A 38 (1984), 41-48. (1984) MR0856623
  9. Hong-Kun Xu, Measures of noncompactness and normal type structures in Banach spaces, Panamer. Math. J. 3 (1993), 17-34. (1993) Zbl0846.46008MR1216273
  10. Köthe G., Topological Vector Spaces I, Springer Veralg, Berlin, 1969. MR0248498
  11. Lindenstrauss J., Tzafiri L., Classical Banach Spaces, Springer Verlag, Berlin, 1973. MR0415253
  12. Montesinos V., Drop property equals reflexivity, Studia Math. 87 (1987), 93-110. (1987) Zbl0652.46009MR0924764
  13. Rolewicz S., On drop property, Studia Math. 85 (1987), 27-35. (1987) MR0879413

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