We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.
@article{bwmeta1.element.bwnjournal-article-smv109i2p197bwm, author = {Shutao Chen and Huiying Sun}, title = {Reflexive Orlicz spaces have uniformly normal structure}, journal = {Studia Mathematica}, volume = {108}, year = {1994}, pages = {197-208}, zbl = {0830.46022}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv109i2p197bwm} }
Chen, Shutao; Sun, Huiying. Reflexive Orlicz spaces have uniformly normal structure. Studia Mathematica, Tome 108 (1994) pp. 197-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv109i2p197bwm/
[00000] [1] J. S. Bae, Reflexivity of a Banach space with a uniformly normal structure, Proc. Amer. Math. Soc. 90 (1984), 269-270. | Zbl 0548.46014
[00001] [2] L. P. Belluce, W. A. Kirc and E. F. Steiner, Normal structure in Banach spaces, Pacific J. Math. 26 (1968), 433-440. | Zbl 0164.15001
[00002] [3] E. Casini and E. Maluta, Fixed point of uniformly Lipschitzian mapping in spaces with uniformly normal structure, Nonlinear Anal. 104 (1984), 285-292.
[00003] [4] S. Chen and Y. Duan, Normal structure and weakly normal structure of Orlicz spaces, Comment. Math. Univ. Carolinae 32 (1991), 219-225. | Zbl 0760.46023
[00004] [5] A. Kamińska, On uniform convexity of Orlicz spaces, Indag. Math. 44 (1982), 27-36. | Zbl 0489.46025
[00005] [6] M. A. Krasnosel'skiĭ and Ya. B. Rutitskiĭ, Convex Functions and Orlicz Spaces, Nauka, Moscow, 1958 (in Russian).
[00006] [7] T. Landes, Normal structure and weakly normal structure of Orlicz sequence spaces, Trans. Amer. Math. Soc. 285 (1981), 523-533. | Zbl 0594.46010
[00007] [8] S. Wang, Differentiability of Carathéodory operators, Sci. Bull. Math. 25 (1980), 42-45.
[00008] [9] T. Wang and B. Wang, Normal structure and sum-property of Orlicz sequence spaces, Chinese Math. Research & Exposition 12 (3) (1992).
[00009] [10] C. Wu, T. Wang, S. Chen and Y. Wang, Geometrical Theory of Orlicz Spaces, Harbin Inst. of Tech. Press, 1986 (in Chinese).