Approximative compactness and Asplund property in Banach function spaces and in Orlicz-Bochner spaces in particular with application

作者：Shang, Shaoqiang^*; Cui, Yunan

来源：Journal of Mathematical Analysis and Applications, 2015, 421(2): 1377-1395.

DOI：10.1016/j.jmaa.2014.07.054

• Approximative compactness
• Asplund space
• Radon-Nikodym property
• Banach space
• Orlicz-Bochner function space

In this paper it is shown that: (1) If every weak* hyperplane of X* is approximatively compact, then (a) X is an Asplund space; (b) X* has the Radon Nikodym property. (2) Criteria for approximative compactness of every weakly* hyperplane of Orlicz Bochner function spaces equipped with the Orlicz norm are given. (3) If X has a Frechet differentiable norm, then (a) Orlicz Bochner function spaces L-M(0) (X*) have the Radon Nikodym property if and only if M is an element of Delta(2); (b) Orlicz Bochner function spaces E-N (X) are Asplund spaces if and only if M is an element of Delta(2). (4) We give an important application of approximative compactness to the theory of generalized inverses for operators between Banach spaces and Orlicz Bochner function spaces.

• 出版日期2015-1-15
• 单位哈尔滨学院; 东北林业大学