The Uniform Boundedness Principle - Dr Joel Feinstein
3,959 views · Published 14 July 2010 · 21:36 · Indexed 17 October 2026
Channel: University of Nottingham · 2010 · Education
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 discusses two famous results concerning collections of bounded linear operators, one of which is a corollary of the other. Both of these results have been called the Banach-Steinhaus Theorem (by various authors). The stronger of these two results is the one which is also known as the Uniform Boundedness Principle. This material is suitable for those with a good background knowledge of metric spaces and normed spaces. In particular, the student should know about bounded (continuous) linear operators between normed spaces, and the Baire Category Theorem for complete metric spaces.
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