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 $r>0$.

Title	Banach-Krein-Šmulian theorem
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