A note on fréchet-montel spaces

Mikael Lindström*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

Let E be a Fréchet space and let Cb(E) denote the vector space of all bounded continuous functions on E. It is shown that the following statements are equivalent: (i) E is Montel. (ii) Every bounded continuous function from E into Co maps every absolutely convex closed bounded subset of E into a relatively compact subset c0. (iii) Every sequence in Cb(E) that converges to zero in the compact-open topology also converges uniformly to zero on absolutely convex closed bounded subsets of E.

Original languageEnglish
Pages (from-to)191-196
Number of pages6
JournalProceedings of the American Mathematical Society
Volume108
Issue number1
DOIs
Publication statusPublished - Jan 1990
MoE publication typeA1 Journal article-refereed

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