Bochner-Lebesgue空间内的最佳同时逼近（英文）  

Best Simultaneous Approximations in Bochner-Lebesgue Spaces

作　　者：魏海花 徐景实[1] 

机构地区：[1]海南师范大学数学与统计学院,海口571158

出　　处：《工程数学学报》2017年第5期563-570,共8页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11361020)

摘　　要：在本文中,我们研究了Bochner-Lebesgue空间内的相对于欧氏空间的Minkowski范数的最佳同时逼近.首先,给出了由距离函数表示的最佳同时逼近的刻画.然后,利用可测选择定理证明其函数取值于一个闭的可分子空间的Bochner-Lebesgue空间,其同时可逼近性等价于此闭的可分子空间的同时可逼近性.最后,指出子空间的可分性是同时可逼近性等价的必要条件.In this paper, we consider the best simultaneous approximations in BochnerLebesgue spaces with respective to Minkowski＇ norms in Euclidean spaces. Firstly,we give a characterization of best simultaneous approximations by the distance functions. Then, by applying this characterization and a measurable selection theorem we show the simultaneous proximinality of a Bochner-Lebesgue space whose functions take values in a closed separable subspace is equivalent to the simultaneous proximinality of the closed separable subspace. Finally, we conclude that for their equivalence, the separability of the subspace is necessary.

关 键 词：Bochner-Lebesgue空间 同时可近性 最佳同时逼近 

分 类 号：O174.4[理学—数学]