Smooth Points of ORLICZ Spaces Equipped with LUXEMBURG Norm
✍ Scribed by R. Grzaślewicz; H. Hudzik
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 630 KB
- Volume
- 155
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
Smooth points of the unit sphere of ORLICZ spaces equipped with LUXEMBURG norm are characterized for a non‐atomic measure as well as for the counting measure. As a corollary, a criterion of smoothness of ORLICZ spaces with LUXEMBURG norm is obtained.
📜 SIMILAR VOLUMES
Rotundity of finite-diii~eilsioiial Orlin spaces 1: equipped with the Luxemburg nomi is considered. It is proved that criteria for rotundity of 1: for 11 2 3 does not depend on 11 and are the same as the criteria for rotundity of the inhite-dimensional subspace h\* of an Orlicz sequence ~p a c e . 1
## Abstract In this paper, we shall give a criteria of the rotundity and uniform rotundity of Orlicz‐Lorentz sequence spaces equipped with the Orlicz norm.
The nonsquare constants in sense of James and Schäffer have the interrelation: CJ (X) • CS(X) = 2 for a Banach space X. For Orlicz sequence and function spaces equipped with Luxemburg norm, the representation of CJ and CS were obtained ([6], [7]). In this paper, we show that the nonsquare constants