Talk:Banach-Alaoglu Theorem

I will try to write down a proof this evening, if I find the time. - Giallo (30.1.13, 12:28)


 * Awesome; that'd be greatly appreciated! --Lord_Farin (talk) 11:31, 30 January 2013 (UTC)

I have written a first (much incomplete) outline of the proof. I'll have to work a bit on the proof for the two lemmas, since my source (Royden & Fitzpatrick) is a bit vague about them, but they shouldn't be too hard. Unfortunately I have a couple of exams soon, thus I'll leave it to you until then. By the way, i don't know if this is really the theorem of Banach-Alaoglu or if it should only be named after Alaoglu. This one was proven by Alaoglu, while Banach has shown that if $X$ is separable, then the closed unit ball in $X^*$ is weak* sequentially compact. - Giallo (30.1.13, 21:39)


 * Conway lists it as Alaoglu's Theorem. --Lord_Farin (talk) 21:28, 30 January 2013 (UTC)


 * Ok, I have moved it to the page for Alaoglu's theorem (the discussion, too). - Giallo (30.1.13, 22:45)

I also have written down the true (at least, I hope) Banach-Alaoglu theorem with proof. - Giallo (30.1.13, 23:26)