Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on Fréchet-Montel spaces

Author: Mikael Lindström
Journal: Proc. Amer. Math. Soc. 108 (1990), 191-196
MSC: Primary 46A14; Secondary 46A06
MathSciNet review: 994780
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ E$ be a Fréchet space and let $ {C^b}\left( E \right)$ 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 $ {c_0}$ maps every absolutely convex closed bounded subset of $ E$ into a relatively compact subset $ {c_0}$. (iii) Every sequence in $ {C^b}\left( E \right)$ that converges to zero in the compact-open topology also converges uniformly to zero on absolutely convex closed bounded subsets of $ E$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A14, 46A06

Retrieve articles in all journals with MSC: 46A14, 46A06

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society