A note on Fréchet-Montel paces

Mikael Lindström

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

A note on Fréchet-Montel paces

Mikael Lindström^*

^*Korresponderande författare för detta arbete

Matematik

Forskningsoutput: Tidskriftsbidrag › Artikel › Vetenskaplig › Peer review

2 Citeringar (Scopus)

Sammanfattning

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.

Originalspråk	Engelska
Sidor (från-till)	191-196
Antal sidor	6
Tidskrift	Proceedings of the American Mathematical Society
Volym	108
Nummer	1
DOI	https://doi.org/10.1090/S0002-9939-1990-0994780-8
Status	Publicerad - jan. 1990
MoE-publikationstyp	A1 Tidskriftsartikel-refererad

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A note on Fréchet-Montel paces

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