摘要
本文我们研究了由半范簇｛Ｐ＿Ｔ｜Ｔ∈（Ｅ，Ｅ＿１）在Ｅ上导出的局部凸拓扑σ＿Ｅ（Ｅ＿１），其中Ｐ＿Ｔ（ｘ）＝‖Ｔｘ‖，ｘ∈Ｅ．首先我们给出了拓扑σ＿Ｅ（Ｅ＿１）＝ｗ和σ＿Ｅ（Ｅ＿１）＝‖·‖的等价条件，接着讨论了在σ＿Ｅ（Ｅ＿１）下的紧性与完备性，最后利用空间稠密特征和关于无穷基数幂等的Ｈｅｓｓｅｎｂｅｒｇ定理进一步研究了σ＿Ｅ（Ｅ＿１）与‖·‖的关系，证明了当Ｅ的稠密特征足够大时在Ｗ和‖·‖间有无穷多个σ＿Ｅ（Ｅ＿１）型拓扑．另外我们还得到了关于稠密特征及空间同构的几个结果。
In this paper, We study the locally convex topology σ_E(E_1)defined by the family of seminorms{P_T:T∈y(E,E_1)},where P_T(x)=‖T_x‖,for all x∈ E,on Banach space E.First we give characteristics of σ_E(E_1)=w and σ_E(E_1)=‖·‖Second we discuss compactness and completeness of subsets of E in σ_E(E_1). Finally, using dense characteristics of a space and Hessenbergs theorem we further study the relation between σ_E(E_1)and‖·‖and obtain some results on dense characteristic and isomorphisim of spaces.
出处
《数学杂志》
CSCD
北大核心
1994年第1期117-125,共9页
Journal of Mathematics
关键词
局部凸拓扑
算子
巴拿赫空间
Banach space,locally convex topology,compactness, comple teness,dense characteristic.
