拓扑线性空间中不连续线性泛函的存在问题

THE EXISTENCE PROBLEM OF LINEAR NON-CONTINUOUS FUNCTIONALS ON TOPOLOGICAL LINEAR SPACES

本文在一般的拓扑线性空间中讨论了线性而不连续泛函的存在问题 .当 dim E≥ | u|时得到此问题的正面回答 .导出两个维数相同的空间 ,当某一个有不闭的线性子空间时 。

This paper obtains that if dim E≤|u| , then there exist the linear non continuous functionals on topological linear space E. Moreover, if dim E =dim F , and one of E and F has a non closed subspace, then there exist the non continuous isomorphism between E and F .$$$$