Banach-Alaoglu theorem

Let $X$ be a normed space, and let $X^{*}$ be its dual. Then the closed unit ball of $X^{*}$,

$$\{f\in X^{*}:\parallel f\parallel \le 1\}$$

is compact in the weak-$*$ topology.

Title	Banach-Alaoglu theorem
Canonical name	BanachAlaogluTheorem
Date of creation	2013-03-22 14:48:44
Last modified on	2013-03-22 14:48:44
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	6
Author	Koro (127)
Entry type	Theorem
Classification	msc 46B10
Synonym	Alaoglu’s theorem