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The weak star topology and the BanachAlaoglu theorem
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Video Source: www.youtube.com/watch?v=tFQOwHeIYgQ
This is a lecture from Dr Feinstein's 4th-year module G14FUN Functional Analysis. • • See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the Functional Analysis screencasts blog page at http://wp.me/PosHB-8v • • In this screencast, Dr Feinstein introduces the weak topology on a normed space and the weak star topology on the dual space. He then proves the Banach-Alaoglu theorem, that the closed unit ball of the dual space is weak star compact. • • This material is suitable for those with a basic knowledge of normed spaces and their duals, and of infinite products of topological spaces, including Tychonoff's theorem on arbitrary products of compact topological spaces.
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