有限维Banach空间中完备集的构造

Constructions of Complete Sets in Finite Dimensional Banach Spaces

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.