scholarly journals Locally uniform convexity in Musielak–Orlicz function spaces of Bochner type endowed with the Luxemburg norm

2011 ◽  
Vol 378 (2) ◽  
pp. 432-441 ◽  
Author(s):  
Shaoqiang Shang ◽  
Yunan Cui
Keyword(s):  
Orlicz Function ◽  
Function Spaces ◽  
Uniform Convexity ◽  
Luxemburg Norm

scholarly journals On the weakly strongly exposed property and some smoothness properties of Orlicz spaces

1996 ◽  
Vol 54 (3) ◽  
pp. 431-440
Author(s):  
Yunan Cui ◽  
Henry K. Hudzik ◽  
Hongwei Zhu
Keyword(s):  
Banach Space ◽  
Orlicz Function ◽  
Orlicz Spaces ◽  
Function Spaces ◽  
Luxemburg Norm ◽  
Orlicz Norm ◽  
Dual Property ◽  
Order Continuous

The notion of a weakly strongly exposed Banach space is introduced and it is shown that this property is the dual property of very smoothness. Criteria for this property in Orlicz function spaces equipped with the Orlicz norm are presented. Criteria for strong smoothness and very smoothness of their subspaces of order continuous elements in the case of the Luxemburg norm are also given.

scholarly journals Complex Convexity of Musielak-Orlicz Function Spaces Equipped with thep-Amemiya Norm

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Lili Chen ◽  
Yunan Cui ◽  
Yanfeng Zhao
Keyword(s):  
Unit Ball ◽  
Function Space ◽  
Orlicz Function ◽  
Extreme Points ◽  
Function Spaces ◽  
Strict Convexity ◽  
Uniform Convexity ◽  
Amemiya Norm

The complex convexity of Musielak-Orlicz function spaces equipped with thep-Amemiya norm is mainly discussed. It is obtained that, for any Musielak-Orlicz function space equipped with thep-Amemiya norm when1≤p<∞, complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in above spaces are given. Criteria for complex strict convexity and complex midpoint locally uniform convexity of above spaces are also deduced.

Orlicz Spaces Without Strongly Extreme Points and Without H-Points

1993 ◽  
Vol 36 (2) ◽  
pp. 173-177 ◽  
Author(s):  
Henryk Hudzik
Keyword(s):  
Extreme Point ◽  
Orlicz Space ◽  
Unit Sphere ◽  
Orlicz Function ◽  
Orlicz Spaces ◽  
Extreme Points ◽  
Luxemburg Norm ◽  
Nonatomic Measure

AbstractW. Kurc [5] has proved that in the unit sphere of Orlicz space LΦ(μ) generated by an Orlicz function Φ satisfying the suitable Δ2-condition and equipped with the Luxemburg norm every extreme point is strongly extreme. In this paper it is proved in the case of a nonatomic measure μ that the unit sphere of the Orlicz space LΦ(μ) generated by an Orlicz function Φ which does not satisfy the suitable Δ2-condition and equipped with the Luxemburg norm has no strongly extreme point and no H-point.

scholarly journals On the WM Points of OrIicz Function Spaces Endowed with Luxemburg Norm

1995 ◽  
Vol 8 (2) ◽  
Author(s):  
Minli Li ◽  
Tingfu Wang ◽  
Cuixia Hao
Keyword(s):  
Function Spaces ◽  
Luxemburg Norm
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