A note on Fréchet-Montel paces

Mikael Lindström

doi:10.1090/S0002-9939-1990-0994780-8

A note on Fréchet-Montel paces

Mikael Lindström^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-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 C^b(E) that converges to zero in the compact-open topology also converges uniformly to zero on absolutely convex closed bounded subsets of E.

Original language	English
Pages (from-to)	191-196
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	108
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1990-0994780-8
Publication status	Published - Jan 1990
MoE publication type	A1 Journal article-refereed

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title = "A note on Fr{\'e}chet-Montel paces",

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AB - 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.

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A note on Fréchet-Montel paces

Abstract

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