Stable Banach spaces, random measures and Orlicz function spaces

1982 ◽  
pp. 121-175 ◽  
Author(s):  
D. J. H. Garling
Keyword(s):  
Banach Spaces ◽  
Orlicz Function ◽  
Function Spaces ◽  
Random Measures

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 Approximative Compactness and Radon-Nikodym Property inw∗Nearly Dentable Banach Spaces and Applications

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Shaoqiang Shang ◽  
Yunan Cui
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Generalized Inverse ◽  
Orlicz Function ◽  
Function Spaces ◽  
Inverse Theory ◽  
Nikodym Property ◽  
Projector Operator ◽  
Approximative Compactness

Authors definew∗nearly dentable Banach space. Authors study Radon-Nikodym property, approximative compactness and continuity metric projector operator inw∗nearly dentable space. Moreover, authors obtain some examples ofw∗nearly dentable space in Orlicz function spaces. Finally, by the method of geometry of Banach spaces, authors give important applications ofw∗nearly dentability in generalized inverse theory of Banach space.

scholarly journals Strongly Extreme Points and Middle Point Locally Uniformly Convex in Orlicz Spaces Equipped with s-Norm

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Yunan Cui ◽  
Yujia Zhan
Keyword(s):  
Banach Spaces ◽  
Orlicz Space ◽  
Necessary Conditions ◽  
Orlicz Function ◽  
Orlicz Spaces ◽  
Extreme Points ◽  
Uniformly Convex ◽  
Middle Point ◽  
Sufficient And Necessary Conditions

As is well known, the extreme points and strongly extreme points play important roles in Banach spaces. In this paper, the criterion for strongly extreme points in Orlicz spaces equipped with s-norm is given. We complete solved criterion-Orlicz space that generated by Orlicz function. And the sufficient and necessary conditions for middle point locally uniformly convex in Orlicz spaces equipped with s-norm are obtained.

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