Geodesic
A Dual characterization of Banach Spaces With the Convex Point-of-Continuity Property
Canadian mathematical bulletin, Tome 32 (1989) no. 3, pp. 274-280

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

We introduce a new type of differentiability, called cofinite Fréchet differentiability. We show that the convex point-of-continuity property of Banach spaces is dual to the cofinite Fréchet differentiability of all equivalent norms. A corresponding result for dual spaces with the weak* convex point-of-continuity property is also established. 
Hare, D. E. G. A Dual characterization of Banach Spaces With the Convex Point-of-Continuity Property. Canadian mathematical bulletin, Tome 32 (1989) no. 3, pp. 274-280. doi: 10.4153/CMB-1989-040-0
@article{10_4153_CMB_1989_040_0,
     author = {Hare, D. E. G.},
     title = {A {Dual} characterization of {Banach} {Spaces} {With} the {Convex} {Point-of-Continuity} {Property}},
     journal = {Canadian mathematical bulletin},
     pages = {274--280},
     year = {1989},
     volume = {32},
     number = {3},
     doi = {10.4153/CMB-1989-040-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-040-0/}
}
TY  - JOUR
AU  - Hare, D. E. G.
TI  - A Dual characterization of Banach Spaces With the Convex Point-of-Continuity Property
JO  - Canadian mathematical bulletin
PY  - 1989
SP  - 274
EP  - 280
VL  - 32
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-040-0/
DO  - 10.4153/CMB-1989-040-0
ID  - 10_4153_CMB_1989_040_0
ER  - 
%0 Journal Article
%A Hare, D. E. G.
%T A Dual characterization of Banach Spaces With the Convex Point-of-Continuity Property
%J Canadian mathematical bulletin
%D 1989
%P 274-280
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-040-0/
%R 10.4153/CMB-1989-040-0
%F 10_4153_CMB_1989_040_0

[1] 1. Asplund, E., Fréchet differentiability of convex functions, Acta Math. 121 (1968), 735–750. Google Scholar

[2] 2. Bourgain, J., Dentability and finite-dimensional decompositions, Studia Math. 67 (1980), 135–148. Google Scholar

[3] 3. Cudia, D., The geometry of Banach spaces. Smoothness, Trans. Amer. Math. Soc. 110 (1964), 284– 314. Google Scholar

[4] 4. Deville, R., G. Godefroy, D. E. G. Hare and V. Zizler, Differentiability of convex functions and the convex point of continuity property in Banach spaces, Israel J. Math., 59 (1957), 245–255. Google Scholar

[5] 5. Diestel, J. and Uhl, J. J. Jr., Vector Measures, Math Surveys, No. 15, American Math Society, Providence, R. I., 1977. Google Scholar

[6] 6. Ghoussoub, N., Maurey, B. and W. Schachermayer, Geometrical implications of certain infinite dimensional decompositions, to appear. Google Scholar

[7] 7. Huff, R. E. and P. D. Morris, Geometric characterizations of the Radon-Nikodym property in Banach spaces, Studia Math. 56 (1976), 157–164. Google Scholar

[8] 8. John, K. and V. Zizler, A note on strong differentiability spaces, Comment. Math. Univ. Carolinae 17 (1976), 127–134. Google Scholar

[9] 9. Namioka, I. and R. R. Phelps, Banach spaces which are Asplund spaces, Duke Math. J. 42 (1975), 735–750. Google Scholar

[10] 10. Phelps, R. R., Dentability and extreme points in Banach spaces, J. Funct. Anal. 17 (1974), 78–90. Google Scholar

[11] 11. Smuljan, V., Sur la dérivabilité de la norme dans l'espace de Banach, Dokl. Akad. Nauk SSSR 27 (1940), 643–648. Google Scholar

[12] 12. Stegall, C., The Radon-Nikodym property in conjugate Banach spaces, II, Trans. Amer. Math. Soc. 206 (1975), 213–223. Google Scholar

Cité par Sources :