无穷维赋范线性空间上单的无界线性算子的存在性

Existence of Unbounded Linear Injector on any Infinite Dimensional Normed Space

利用Zorn引理证明了任何无穷维赋范线性空间上都存在单的无界线性算子,从而得出Banach空间上的具有闭的零子空间的线性算子未必有界.

By Zorn lemma, it has been proved that there is an unbounded linear injector on any infinite dimensional normed space, therefore it gives that a linear operator which has closed null subspace on Banach space is sometimes unbounded and sometimes bounded.