Equivalence of the properties ($\beta$) and (NUC) in Orlicz spaces
Dhompongsa, Sompong
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000), p. 449-457 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 2000-01-01
Classification:  46B20,  46E30,  46E40
@article{119180,
     author = {Sompong Dhompongsa},
     title = {Equivalence of the properties ($\beta$) and (NUC) in Orlicz spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {41},
     year = {2000},
     pages = {449-457},
     zbl = {1040.46026},
     mrnumber = {1795076},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119180}
}
Dhompongsa, Sompong. Equivalence of the properties ($\beta$) and (NUC) in Orlicz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 449-457. http://gdmltest.u-ga.fr/item/119180/

Chen S. Geometry of Orlicz spaces, Dissertationes Mathematicae 356, Warszawa, 1996. | MR 1410390 | Zbl 1089.46500

Clarkson J.A. Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396-414. (1936) | MR 1501880 | Zbl 0015.35604

Cui Y.; Pluciennik R.; Wang T. On property $(\beta)$ in Orlicz spaces, Arch. Math. 68 (1997), 1-13. (1997) | MR 1452160 | Zbl 0894.46023

Huff R. Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 473-549. (1980) | MR 0595102 | Zbl 0505.46011

Kutzarova D.N. A nearly uniformly convex space which is not a $(\beta)$ space, Acta Univ. Carolinae Math. Phys. 30 (1989), 95-98. (1989) | MR 1046453 | Zbl 0715.46006

Kutzarova D.N. An isomorphic characterization of property $(\beta)$ of Rolewicz, Note Mat. 10.2 (1990), 347-354. (1990) | MR 1204212 | Zbl 0789.46009

Kutzarova D.N. On condition $(\beta)$ and $\Delta$-uniform convexity, C.R. Acad. Bulgar Sci. 42.1 (1989), 15-18. (1989) | MR 0991453 | Zbl 0696.46017

Montesinos V. Drop property equals reflexivity, Studia Math. 87 (1987), 93-100. (1987) | MR 0924764 | Zbl 0652.46009

Montesinos V.; Torregrosa J.R. A uniform geometric property of Banach spaces, Rocky Mountain J. Math. 22.2 (1992), 683-690. (1992) | MR 1180730 | Zbl 0788.46020

Musielak J. Orlicz spaces and modular spaces, LNM 1034, pp.1-222, Berlin-Heidelberg-New York (1983). (1983) | MR 0724434 | Zbl 0557.46020

Rolewicz S. On drop property, Studia Math. 85 (1987), 27-35. (1987) | MR 0879413

Rolewicz S. On $\Delta$-uniform convexity and drop property, Studia Math. 87 (1987), 181-191. (1987) | MR 0928575 | Zbl 0652.46010