Previous |  Up |  Next

Article

Keywords:
Orlicz spaces; property $(\beta)$; property (NUC)
Summary:
We obtain the equivalence of the properties $(\beta )$ and (NUC) in Orlicz function spaces. This answers a question raised by Y. Cui, R. Pluciennik and T. Wang.
References:
[1] Chen S.: Geometry of Orlicz spaces. Dissertationes Mathematicae 356, Warszawa, 1996. MR 1410390 | Zbl 1089.46500
[2] Clarkson J.A.: Uniformly convex spaces. Trans. Amer. Math. Soc. 40 (1936), 396-414. MR 1501880 | Zbl 0015.35604
[3] Cui Y., Pluciennik R., Wang T.: On property $(\beta)$ in Orlicz spaces. Arch. Math. 68 (1997), 1-13. MR 1452160 | Zbl 0894.46023
[4] Huff R.: Banach spaces which are nearly uniformly convex. Rocky Mountain J. Math. 10 (1980), 473-549. MR 0595102 | Zbl 0505.46011
[5] Kutzarova D.N.: A nearly uniformly convex space which is not a $(\beta)$ space. Acta Univ. Carolinae Math. Phys. 30 (1989), 95-98. MR 1046453 | Zbl 0715.46006
[6] Kutzarova D.N.: An isomorphic characterization of property $(\beta)$ of Rolewicz. Note Mat. 10.2 (1990), 347-354. MR 1204212 | Zbl 0789.46009
[7] Kutzarova D.N.: On condition $(\beta)$ and $\Delta$-uniform convexity. C.R. Acad. Bulgar Sci. 42.1 (1989), 15-18. MR 0991453 | Zbl 0696.46017
[8] Montesinos V.: Drop property equals reflexivity. Studia Math. 87 (1987), 93-100. MR 0924764 | Zbl 0652.46009
[9] Montesinos V., Torregrosa J.R.: A uniform geometric property of Banach spaces. Rocky Mountain J. Math. 22.2 (1992), 683-690. MR 1180730 | Zbl 0788.46020
[10] Musielak J.: Orlicz spaces and modular spaces. LNM 1034, pp.1-222, Berlin-Heidelberg-New York (1983). MR 0724434 | Zbl 0557.46020
[11] Rolewicz S.: On drop property. Studia Math. 85 (1987), 27-35. MR 0879413
[12] Rolewicz S.: On $\Delta$-uniform convexity and drop property. Studia Math. 87 (1987), 181-191. MR 0928575 | Zbl 0652.46010
Partner of
EuDML logo