距离线性空间上的非零连续线性泛函的存在条件

The Existence Conditions of Non-zero Continuous Linear Functional in Linear Distance Space

在非零的赋范线性空间上,总存在非零的连续线性泛函.但是对一般的距离线性空间,这不一定成立.那么这个性质在距离线性空间中成立需要什么条件呢?本文按照这个思路,对距离线性空间上的非零连续线性泛函的存在条件进行了探讨,并找到了在距离线性空间上成立的条件.

The continuous non-zero linear functional always exists in normed linear space,but this character may not be true in linear distance space.Then,what kinds of conditions must be met to ensure this character in the linear distance space？ In accordance with this idea,the existence conditions of non-zero continuous linear functional in linear distance space were discussed and the necessary conditions were given in this paper.