无穷序列空间上紧性问题探讨

Discussion on the Compactness in Space of Infinite Sequences

紧性概念是泛函分析的重要内容,在现代分析学中应用广泛;考虑l^p,p≥2空间上的集合紧性问题,证明了Ml^p为预紧集的重要条件是M一致有界且一致收敛,并给出了一个应用实例.

The notion of compactness, which is an important content in functional analysis, is widely used in modem analytical science. In this article, the compactness of set is discussed in l^p ,p ≥ 2. It is proved that M■l^p is pre-compact set in Ip if and only if M is uniformly bounded and uniformly convergent. As an application, an example is presented here.