Previous |  Up |  Next

Article

Keywords:
Orlicz spaces; uniformly normal structure
Summary:
We prove that in Orlicz spaces endowed with Orlicz norm the uniformly normal structure is equivalent to the reflexivity.
References:
[1] Belluce L.P., Kirk W.A., Steiner E.F.: Normal structure in Banach spaces. Pacific J. Math. 26 (1968), 433-440. MR 0233178 | Zbl 0164.15001
[2] Bae J.S.: Reflexivity of a Banach space with a uniformly normal structure. Proc. Amer. Math. Soc. 90 (1984), 269-270. MR 0727247 | Zbl 0548.46014
[3] Landes T.: Normal structure and weakly normal structure of Orlicz sequence spaces. Trans. AMS 285 (1984), 523-533. MR 0752489 | Zbl 0594.46010
[4] Tingfu Wang, Baoxiang Wang: Normal structure ad sum-property and LD property of Orlicz spaces. J. Math. Res. Exp. 12 (1992), 477-478.
[5] Shutao Chen, Yanzheng Duan: Normal structure and weakly normal structure of Orlicz space s. Comment. Math. Univ. Carolinae 32 (1991), 219-225. MR 1137782
[6] Shutao Chen, Huiying Sun: Reflexive Orlicz spaces have uniformly normal structure. to appear. MR 1269776
[7] Krasnoselskii M.A., Rutickii Ya.B.: Convex Functions and Orlicz Spaces. Moscow, 1958.
[8] Wu C., Wang T., Chen S., Wang Y.: Geometry of Orlicz Spaces. H.I.T. Press, Harbin, 1986.
[9] Shutao Chen: Some rotundities of Orlicz spaces with Orlicz norm. Bull. Polish Academy Sci. Math. 34 (1986), 585-596. MR 0884206
Partner of
EuDML logo