摘要
在第1节中讨论了σ(E_1)拓扑的性质,主要结果是证明了σ(E_1)和一个极族所导入的极拓扑相等。作为应用,在第2节中证明了自反情况下的Krein—Smulian定理。
We have discussed the properties of topology σ(E_1)in section one.The main results are to prove the equality of topology σ(E_1)and a polar topology which are reduced by a polar family.The elements of this polar family are absolutely convex and absorbing(norm)bounded closed subsets of E_1.As the application of σ(E_1),we have shown the excellent Krein-Smulian theorem for reflexive Banach space E.
出处
《河南师范大学学报（自然科学版）》
CAS
CSCD
1990年第1期1-4,共4页
Journal of Henan Normal University(Natural Science Edition)
关键词
拓扑向量空间
极拓扑
弱拓扑
topological vector spaces
polar topology
weak topology
