核局部凸空间的一个新特征

A NEW CHARACTERIZATION OF NUCLEAR LOCALLY CONVEX SPACES

Ａ．Ｐｉｅｔｓｃｈ［１］在讨论核局部凸空间时给出了两类矢值序列空间ｌ１［Ｘ］和ｌ１｛Ｘ｝．本文建立了矢值序列空间ｌ１［Ｘ］及ｌ１｛Ｘ｝和连续线性算子空间Ｌ（ｃ０，Ｘ）及绝对可和算子空间ＡＳ（ｃ０，Ｘ）之间的拓扑同胚关系．通过ｃ０上的矢值算子类Ｌ（ｃ０，Ｘ）和ＡＳ（ｃ０，Ｘ）及其上的拓扑等价关系。

In this paper , the topological homeomorphism relations between the summable sequence spaces on a locally convex space X and operator spaces from c 0 to X are given. By use of them, a new characterization of nuclear locally convex spaces is presented in this paper.