Geodesic
Mazur Intersection Properties for Compact and Weakly Compact Convex Sets
Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 225-230

Voir la notice de l'article provenant de la source Cambridge University Press

Various authors have studied when a Banach space can be renormed so that every weakly compact convex, or less restrictively every compact convex set is an intersection of balls. We first observe that each Banach space can be renormed so that every weakly compact convex set is an intersection of balls, and then we introduce and study properties that are slightly stronger than the preceding two properties respectively.
DOI : 10.4153/CMB-1998-032-8
Mots-clés : 46B03, 46B20, 46A55 
Vanderwerff, Jon. Mazur Intersection Properties for Compact and Weakly Compact Convex Sets. Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 225-230. doi: 10.4153/CMB-1998-032-8
@article{10_4153_CMB_1998_032_8,
     author = {Vanderwerff, Jon},
     title = {Mazur {Intersection} {Properties} for {Compact} and {Weakly} {Compact} {Convex} {Sets}},
     journal = {Canadian mathematical bulletin},
     pages = {225--230},
     year = {1998},
     volume = {41},
     number = {2},
     doi = {10.4153/CMB-1998-032-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-032-8/}
}
TY  - JOUR
AU  - Vanderwerff, Jon
TI  - Mazur Intersection Properties for Compact and Weakly Compact Convex Sets
JO  - Canadian mathematical bulletin
PY  - 1998
SP  - 225
EP  - 230
VL  - 41
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-032-8/
DO  - 10.4153/CMB-1998-032-8
ID  - 10_4153_CMB_1998_032_8
ER  - 
%0 Journal Article
%A Vanderwerff, Jon
%T Mazur Intersection Properties for Compact and Weakly Compact Convex Sets
%J Canadian mathematical bulletin
%D 1998
%P 225-230
%V 41
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-032-8/
%R 10.4153/CMB-1998-032-8
%F 10_4153_CMB_1998_032_8

[1] 1. Borwein, J. and Fabian, M., On convex functions having points of Gateaux differentiability which are not points of Fréchet differentiability. Canad. J. Math. 45 (1993), 1121–1134. Google Scholar

[2] 2. Borwein, J. and Fitzpatrick, S., A weak Hadamard smooth renorming of L(Ω, ñ). Canad. Math. Bull. 36 (1993), 407–413. Google Scholar

[3] 3. Deville, R., Godefroy, G. and Zizler, V., Smoothness and Renormings in Banach Spaces. PitmanMonographs and Surveys in Pure and Applied Math. 64, Longman, 1993. Google Scholar

[4] 4. Giles, J. R., Gregory, D. A. and Sims, B., Characterisation of normed linear spaces withMazur's intersection property. Bull. Austral. Math. Soc. 18 (1978), 105–123. Google Scholar

[5] 5. Sevilla, M. Jiménez and Moreno, J. P., Renorming Banach spaces with the Mazur intersection property. J. Funct. Anal. 144 (1997), 486–504. Google Scholar

[6] 6. Mazur, S., Uber schwach konvergenz in der raumen (L). Studia Math. 4 (1933), 128–133. Google Scholar

[7] 7. Phelps, R. R., A representation theorem for bounded convex sets. Proc. Amer. Math. Soc. 11(1960), 976–983. Google Scholar

[8] 8. Pličko, A. N., Some properties of the Johnson-Lindenstrauss space. Functional Anal. Appl. 15 (1981), 88–89. Google Scholar

[9] 9. Pličko, A. N., Bases and complements in nonseparable Banach spaces. SiberianMath. J. 25 (1984), 636–641. Google Scholar

[10] 10. Sersouri, A., The Mazur property for compact sets. Pacific J. Math. 133 (1988), 185–195. Google Scholar

[11] 11. Sersouri, A., Mazur's intersection property for finite dimensional sets. Math. Ann. 283 (1989), 165–170. Google Scholar

[12] 12. Singer, I., Basis in Banach Spaces. Vol 2, Springer-Verlag, Berlin, Heidelberg, New York, 1981. Google Scholar

[13] 13. Whitfield, J. and Zizler, V., Mazur's intersection property of balls for compact convex sets. Bull. Austral. Math. Soc. 35 (1987), 267–274. Google Scholar

[14] 14. Zizler, V., Renorming concerning Mazur's intersection property of balls for weakly compact convex sets. Math. Ann. 276 (1986), 61–66. Google Scholar

Cité par Sources :