Geodesic
Smooth Norms in Orlicz Spaces
Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 74-82

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

Equivalent norms with best order of Frechet and uniformly Frechet differentiability in Orlicz spaces are constructed. Classes of Orlicz which admit infinitely many times Frechet differentiable equivalent norm are found.
DOI : 10.4153/CMB-1991-012-7
Mots-clés : 46E30, 46B20 
Maleev, R. P.; Troyanski, S. L. Smooth Norms in Orlicz Spaces. Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 74-82. doi: 10.4153/CMB-1991-012-7
@article{10_4153_CMB_1991_012_7,
     author = {Maleev, R. P. and Troyanski, S. L.},
     title = {Smooth {Norms} in {Orlicz} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {74--82},
     year = {1991},
     volume = {34},
     number = {1},
     doi = {10.4153/CMB-1991-012-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-012-7/}
}
TY  - JOUR
AU  - Maleev, R. P.
AU  - Troyanski, S. L.
TI  - Smooth Norms in Orlicz Spaces
JO  - Canadian mathematical bulletin
PY  - 1991
SP  - 74
EP  - 82
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-012-7/
DO  - 10.4153/CMB-1991-012-7
ID  - 10_4153_CMB_1991_012_7
ER  - 
%0 Journal Article
%A Maleev, R. P.
%A Troyanski, S. L.
%T Smooth Norms in Orlicz Spaces
%J Canadian mathematical bulletin
%D 1991
%P 74-82
%V 34
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-012-7/
%R 10.4153/CMB-1991-012-7
%F 10_4153_CMB_1991_012_7

Akimovich, [A] V. A., On the uniform convexity and uniform smoothness of Orlicz spaces, Teoria functii, func. an. ipriloj. (Kharkov) 15 (1972), 114–121. Google Scholar

Bonic, [BF] R., Frampton, J., Smooth functions on Banach manifolds, J. Math. Mechanics 15(1966), 877-898. Google Scholar

Deville, [Dl] R., A characterization of C°°-smooth Banach spaces, Proceedings of the London Math. Soc, to appear. Google Scholar

[D2] , Geometrical implications of the existence of very smooth bump functions in Banach spaces, Israel J. of Math., to appear. Google Scholar

Godefroy, [GTWZ] G., Troyanski, S., Whitfield, J., Zizler, V., Smoothness in weakly compactly generated Banach spaces, J. Funct. An. 52 (1983), 344–352. Google Scholar

Krasnoselskii, [KR] M. A., Rutickii, Y. B., Convex functions and Orlicz spaces, (in Russian), Moskow, 1958. Google Scholar

[LT1] Lindenstraus, J., Tzafriri, L., Classical Banach spaces I, Sequence Spaces. Springer-Verlag, 1978. Google Scholar

[LT2] Lindenstraus, J., On Orlicz sequence spaces III, Israel J. of Math. 14 (1973), 368–389. Google Scholar

[MT1] Maleev, R. P., Troyanski, S. L., On the moduli of convexity and smoothness in Orlicz spaces, Studia Math. 54 (1975), 131–141. Google Scholar

[MT2] Maleev, R. P. , Smooth functions in Orlicz spaces, Banach Space Theory, Proceedings of a Research Workshop held July 5-25, 1987, Contemporary Mathematics 85 (1989), 355–370. Google Scholar

[S] Sundaresan, K., Smooth Banach spaces, Math. Ann. 173 (1967), 191–199. Google Scholar

[SS] Sundaresan, K., Swaminathan, S., Geometry and Nonlinear Analysis in Banach spaces. Lecture notes in Math., No. 1131, Springer-Verlag, 1985. Google Scholar

Cité par Sources :