在线咨询
中国工业与应用数学学会会刊
主管:中华人民共和国教育部
主办:西安交通大学
ISSN 1005-3085  CN 61-1269/O1

工程数学学报 ›› 2017, Vol. 34 ›› Issue (5): 563-570.doi: 10.3969/j.issn.1005-3085.2017.05.010

• • 上一篇    

Bochner-Lebesgue空间内的最佳同时逼近(英)

魏海花,    徐景实   

  1. 海南师范大学数学与统计学院,海口  571158
  • 收稿日期:2016-02-01 接受日期:2017-03-06 出版日期:2017-10-15 发布日期:2017-12-15
  • 通讯作者: 徐景实 E-mail address: jingshixu@126.com
  • 基金资助:
    国家自然科学基金(11361020).

Best Simultaneous Approximations in Bochner-Lebesgue Spaces

WEI Hai-hua,   XU Jing-shi   

  1. School of Mathematics and Statistics, Hainan Normal University, Haikou 571158
  • Received:2016-02-01 Accepted:2017-03-06 Online:2017-10-15 Published:2017-12-15
  • Contact: J. Xu. E-mail address: jingshixu@126.com
  • Supported by:
    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.

关键词: Bochner-Lebesgue空间, 同时可近性, 最佳同时逼近

Abstract: In this paper, we consider the best simultaneous approximations in Bochner-Lebesgue 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.

Key words: Bochner-Lebesgue space, simultaneously proximinality, best simultaneous approximation

中图分类号: