1990/01/01 by Mikael Lindstr{öm · 1 citation
Mathematics · #Advanced Banach Space Theory #Fixed Point Theorems Analysis #Approximation Theory and Sequence Spaces #Mathematics #Bounded function #Zero (linguistics) #Sequence (biology) #Space (punctuation) #Regular polygon #Uniform boundedness #Combinatorics #Locally convex topological vector space #Uniform continuity #Continuous function (set theory) #Function (biology) #Pure mathematics #Discrete mathematics #Mathematical analysis #Geometry #Computer science #Metric space
paper · pdf · doi:10.1090/s0002-9939-1990-0994780-8
openalex publication_date 1990/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 c0 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.