级数性质与空间有限（无限）维特征

The Properties of Series and Characterizations of Finite(Infinite) Dimensional Banach Spaces

通过讨论实巴拿赫空间中级数的各种性质，刻划空间有限（无限）维特征。证明了每个无限维巴拿赫空间中都有一个闭子空间Ｘ，Ｘ中有级数Σｘｎ满足条件（Ｎ），但其和域Ｓ（｛ｘｎ｝）非凸集。

In this article various properties of series in the real Banach space are discussed.It is proved that in every infinite dimensional Banach space Y there exists a closed subspace X and a series Σxn in X satisfying condition(N)(i.e.xn→0 and for every f∈X,f≠0,there exists a rearrangement{xπ(n)} of{xn}such that Σ f(xπ(n))converges conditionally) with S({xn}),the domain of sum of Σ xn,it is not convex.