有限维Banach空间中完备集的构造  

Constructions of Complete Sets in Finite Dimensional Banach Spaces

作　　者：徐珂 段博韬 XU Ke;DUAN Bo-tao(School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《中北大学学报（自然科学版）》2021年第5期408-411,425,共5页Journal of North University of China(Natural Science Edition)

基　　金：安徽省自然科学基金资助项目(1908085MA05);安徽省高校自然科学研究项目(KJ2019A0590);安徽优秀人才支持计划重点项目(gxyqZD2020022)。

摘　　要：研究了Banach空间完备集构造的问题.对于完备集的构造,Bavaud和Lachand-Robert及Oudet从n维欧氏空间中的完备集出发构造了n+1维欧氏空间中的完备集.Papini和吴森林教授将Bavaud和Lachand-Robert及Oudet的结果推广到Banach空间.基于Papini和吴森林教授的工作,用任意子空间代替超平面,将Bavaud和Lachand-Robert及Oudet的构造法推广到高维的Banach空间中,即从低维的Banach空间中的完备集出发,去构造任意有限维Banach空间中的完备集.The constructions of complete sets in Banach space was investigated.For the constructions of complete sets,Bavaud,Lachand-Robert and Oudet constructed the complete sets in n+1 dimensions Euclidean space from the complete sets in n dimensions Euclidean space.Papini and Professor Wu extended the results of Bavaud’s,Lachand-Robert and Oudet’s to Banach space.Based on the Papini and Professor Wu’s work,the constructions methods of Bavaud’s,Lachand-Robert and Oudet’s were futher extended to high dimensional Banach space by replacing the hyperplane with arbitrary subspace,that is,from the complete sets in lower dimensional Banach space to construct the complete sets in the arbitrary finite dimensional Banach space.

关 键 词：BANACH空间 完备集 完备化集 子空间 超平面 

分 类 号：O177[理学—数学]