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Banach-Alaoglu theorem (Theorem)

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

$\displaystyle \{f\in X^* : \Vert f\Vert\leq 1\}$
is compact in the weak-$ *$ topology.



"Banach-Alaoglu theorem" is owned by Koro.
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Other names:  Alaoglu's theorem

Attachments:
proof of Banach-Alaoglu theorem (Proof) by Mathprof
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Cross-references: topology, compact, unit ball, closed, normed space
There are 2 references to this entry.

This is version 3 of Banach-Alaoglu theorem, born on 2004-11-12, modified 2005-03-17.
Object id is 6471, canonical name is BanachAlaogluTheorem.
Accessed 5128 times total.

Classification:
AMS MSC: 46B10 (Functional analysis :: Normed linear spaces and Banach spaces; Banach lattices :: Duality and reflexivity)
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