Banach-Steinhaus定理的推广

Generalization of banach-steinhaus theorem

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.