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:
[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
[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