Geodesic
Some Geometric Properties in Orlicz Sequence Spaces Equipped with Orlicz Norm
Journal of convex analysis, Tome 6 (1999) no. 1, pp. 91-114.

Voir la notice de l'article provenant de la source Heldermann Verlag

It is proved that for any reflexive Banach space X, both X and X* are CLUR if and only if both X and X* have property H. Criteria for rotundity, local uniform rotundity, compact local uniform rotundity and property H in Orlicz sequence spaces equipped with the Orlicz norm are given. Criteria for property H, rotundity and LUR were already known in the literature only for finitely valued Orlicz functions which vanish only at zero and are N-functions (i.e. they satisfy conditions (01) and (infty1). All our criteria except Corollary 2.15 are given for arbitrary Orlicz functions. Criteria for smoothness of lΦ0 in Corollary 2.15 are given for any finitely valued Orlicz function satisfying condition (infty1), extending the respective result of Chen, Hudzik and Wisla proved only for Orlicz functions vanishing only at zero.
Classification : 46E30, 46E40, 46B20
Mots-clés : Orlicz sequence space, compact local uniform rotundity, property H, smoothness, copy of l-sub-infinity 
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     title = {Some {Geometric} {Properties} in {Orlicz} {Sequence} {Spaces} {Equipped} with {Orlicz} {Norm}},
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Y. Cui; H. Hudzik; M. Nowak; R. Pluciennik. Some Geometric Properties in Orlicz Sequence Spaces Equipped with Orlicz Norm. Journal of convex analysis, Tome 6 (1999) no. 1, pp. 91-114. http://geodesic.mathdoc.fr/item/JCA_1999_6_1_JCA_1999_6_1_a6/