空间X上的有界集族及X*不可距离化的条件

The Relation Between Some Locally Convex Space and Sequence Space and a Metrizable Condition for Strong Dual Space X

在一类局部凸空间 X上构造了有界集族 Δu,讨论了 Δu中有界集的若干性质以及 Δu与数列空间 S的关系 ;由此推广了 И.М.盖尔芳特在《广义函数》( )中给出的几个结论 ;并给出了 X*可赋范的一个充要条件和 X*不可距离化的一个充分条件 .

Let X be a locally convex space with countable semi norm ｛ P n ｝.We produce a family of bounded sets Δ u . Δ u and a set of sequence space S are one to one.Using Δ u ,we generalize some results of Generalized Function,Ⅱ (Γельфанд.И.М) and obtain a metrizable condition for strong dual space X  .