Banach-Steinhaus定理的推广  

Generalization of banach-steinhaus theorem

作　　者：胡去非[1] 闫守峰[1] 

机构地区：[1]华北科技学院基础部,北京东燕郊101601

出　　处：《大庆石油学院学报》2008年第4期104-106,共3页Journal of Daqing Petroleum Institute

基　　金：河北省教育厅自然科学指导项目(Z2006439)

摘　　要：将Banach-Steinhaus定理推广到拓扑向量空间上.设X,Y为拓扑向量空间,X是第二纲的,若AB0逐点有界,则A是等度连续的.B0表示X到Y的连续线性算子组成的向量空间.In this paper, Banach-Steinhans theorem in the functional analysis is generalized to the topological vector space. Supposed X and Y are both topological vector spaces and X is of the second category, if0 is pointwise bounded, then must be equicontinuous. Here0 is a topological vector space composed of continuous linear operator.

关 键 词：拓扑向量空间 完备 第二纲集 逐点有界 等度连续 

分 类 号：O177.3[理学—数学]