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 Cb(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 |
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Sidor (från-till) | 191-196 |
Antal sidor | 6 |
Tidskrift | Proceedings of the American Mathematical Society |
Volym | 108 |
Nummer | 1 |
DOI | |
Status | Publicerad - jan. 1990 |
MoE-publikationstyp | A1 Tidskriftsartikel-refererad |