拟速完备性与网状空间的诱导极限(英文)

Quasi Fast Completeness and Inductive Limits of Webbed Spaces

英文关键词:locally convex spaces  inductive limits  webbed spaces.

中文摘要:

      设（Ｅ，ζ）＝ｉｎｄｌｉｍ（Ｅ_n，ζ_n）为局部凸空间的诱导极限．称（ＤＳＴ）成立若（Ｅ，ζ）中每个有界集含于且有界于某（Ｅ_n，ζ_n）．引进一种弱于速完备性的性质，叫做拟速完备性，并证明了对于严格网状空间的诱导极限，拟速完备性蕴涵（ＤＳＴ）．利用ＤｅＷｉｌｄｅ的理论，也给出了关于（ＤＳＴ）的其他条件．这些结果改进了已有的有关结论

英文摘要:

      Let (E,ζ)= indlim (E_n ,ζ_n) be an inductive limit of locally convex spaces. We say that ( DST ) holds if each bounded set in (E,ζ) is contained and bounded in some (E_n,ζ_n). We introduce a property which is weaker than fast completeness, quasi-fast completeness, and prove that for inductive limits of strictly webbed spaces, quasi-fast completeness implies that ( DST ). By using De Wilde’s theory on webbed spaces,we also give some other conditions for (DST). These results improve relevant earlier results