scholarly journals Smoothness of the Orlicz norm in Musielak-Orlicz function spaces

2013 ◽  
Vol 287 (8-9) ◽  
pp. 1025-1041 ◽  
Author(s):  
Rui F. Vigelis ◽  
Charles C. Cavalcante
Keyword(s):  
Orlicz Function ◽  
Function Spaces ◽  
Orlicz 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 Extreme Points and Rotundity in Musielak-Orlicz-Bochner Function Spaces Endowed with Orlicz Norm

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Shaoqiang Shang ◽  
Yunan Cui ◽  
Yongqiang Fu
Keyword(s):  
Extreme Point ◽  
Orlicz Function ◽  
Extreme Points ◽  
Function Spaces ◽  
Orlicz Norm

The criteria for extreme point and rotundity of Musielak-Orlicz-Bochner function spaces equipped with Orlicz norm are given. Although criteria for extreme point of Musielak-Orlicz function spaces equipped with the Orlicz norm were known, we can easily deduce them from our main results.

Kadec-Klee property in Musielak-Orlicz function spaces equipped with the Orlicz norm

2021 ◽  
Author(s):  
Yunan Cui ◽  
Li Zhao
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Orlicz Function ◽  
Function Spaces ◽  
Fixed Point Property ◽  
Point Property ◽  
Orlicz Norm

AbstractIt is well-known that the Kadec-Klee property is an important property in the geometry of Banach spaces. It is closely connected with the approximation compactness and fixed point property of non-expansive mappings. In this paper, a criterion for Musielak-Orlicz function spaces equipped with the Orlicz norm to have the Kadec-Klee property are given. As a corollary, we obtain that a class of non-reflexive Musielak-Orlicz function spaces have the Fixed Point property.

scholarly journals Isomorphic copies of $$l^\infty $$ l ∞ in Cesàro–Orlicz function spaces

Positivity ◽  
2016 ◽  
Vol 21 (3) ◽  
pp. 1015-1030 ◽  
Author(s):  
Tomasz Kiwerski ◽  
Paweł Kolwicz
Keyword(s):  
Orlicz Function ◽  
Function Spaces
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