关于Riesz引理的注记

An remark on Riesz lemma

研究了经典形式的Riesz引理的应用及特殊情形下Riesz引理的表述问题。利用Riesz引理给出了一个判定赋范线性空间是有限维的方法。在赋范线性空间的真子空间与有限维空间线性同胚的条件下,给出了Riesz引理的表述形式。

We study the application of the Riesz lemma and its representation under special conditions. We give a method to judge a normed linear space whether it has finite dimension through the Riesz lemma. We give a special representation of Riesz lemma under the condition that it has a subspace to be homeomorphous to a finite dimension space.