A necessary and sufficient condition for $w^ *$-bounded sets to be strongly bounded
HTML articles powered by AMS MathViewer
- by Carlos Bosch and Jan Kucera PDF
- Proc. Amer. Math. Soc. 101 (1987), 453-454 Request permission
Abstract:
It is known that if a locally convex space $E$ is quasi-complete then every $\sigma (Eβ,E)$-bounded set in $Eβ$ is $\beta (Eβ,E)$-bounded. This result cannot be reversed. Here we show that every $\sigma (Eβ,E)$-bounded set is $\beta (Eβ,E)$-bounded iff $E$ is fast complete.References
-
Marc de Wilde, Closed graph theorems and webbed spaces, Pitman, London, 1978.
- Helmut H. Schaefer, Topological vector spaces, Graduate Texts in Mathematics, Vol. 3, Springer-Verlag, New York-Berlin, 1971. Third printing corrected. MR 0342978, DOI 10.1007/978-1-4684-9928-5
- Albert Wilansky, Modern methods in topological vector spaces, McGraw-Hill International Book Co., New York, 1978. MR 518316
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 453-454
- MSC: Primary 46A05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0908647-4
- MathSciNet review: 908647