A note on fréchet-montel spaces

Mikael Lindström*

*Korresponderande författare för detta arbete

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2 Citeringar (Scopus)


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.

Sidor (från-till)191-196
Antal sidor6
TidskriftProceedings of the American Mathematical Society
StatusPublicerad - jan 1990
MoE-publikationstypA1 Tidskriftsartikel-refererad


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