拓扑线性空间中的收敛性

The Convergence in Topological Linear Space

本文利用向量拓扑空间上的新的拓扑结构,研究了拓扑线性空间收敛的若干性质,即弱收敛与σ(y)收敛的关系,并给出了弱收敛的一个等价形式,弱拓扑可以由所有形如:{x∈X:|g(Tx)|<ε,T∈B(X,Y),g∈Y′}为局部邻域子基所产生的拓扑。

In this paper,we study some properties of convergence in Topologicpl Linear Space (TPS)by introducing a new topological Conslfructure of TPS. Wediscuss the relations between the Weak Convergence and σ(Y) Convergence and obtain a equivalent form of weak couvergence,it is that Weak topologic can be founded by taking all set of form {x∈X: |g(Tx)|<ε, T∈B[X,Y],g∈Y} aslocalneighborhood subbase.