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Album: Advanced Mathematics

Track: The weak star topology and the Banach-Alaoglu theorem

Maths-advanced

Description: 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.

Keywords: maths, mathematics, level 4, level5, postgraduate, masters, advanced

Author: The University of Nottingham

Category: Mathematics

Web page: http://www.nottingham.ac.uk/mathematics

Thumbnail: http://itunesu.nottingham.ac.uk/media/Mathematics/MathsAdvanced/images/maths-advanced.jpg

Track media file: http://itunesu.nottingham.ac.uk/media/Mathematics/MathsAdvanced/video/FUN-190310.mp4

Duration: 43:01

Size: 20167000

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