Banach-Krein-Šmulian theorem
Let $E$ be a Banach space^{}. A convex subset $C$ of the dual space^{} ${E}^{*}$ is closed in the weak-$*$ topology^{} if and only if the intersection^{} of $C$ with the ball ${B}_{r}(0)$ is weak-$*$ closed for every $r>0$.
References
- 1 Dunford, N., and J. T. Schwartz, Linear Operators, Part I, Interscience Publishers, 1967.
Title | Banach-Krein-Šmulian theorem |
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Canonical name | BanachKreinvSmulianTheorem |
Date of creation | 2013-03-22 15:14:52 |
Last modified on | 2013-03-22 15:14:52 |
Owner | georgiosl (7242) |
Last modified by | georgiosl (7242) |
Numerical id | 21 |
Author | georgiosl (7242) |
Entry type | Theorem |
Classification | msc 46H05 |