The Uniform Boundedness Principle

My screencast on the Uniform Boundedness Principle (which some call the Banach-Steinhaus Theorem) is available from
This is one of the screencasts (video with synchronized audio) from my level 4 module G14FUN Functional Analysis. (See also the complete set of G!4FUN screencasts available from )

There is some inconsistency in the literature over which theorem should be called the Banach-Steinhaus Theorem. In this screencast I cover two results, 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 the two results is the one which is also known as the Uniform Boundedness Principle.


One response to “The Uniform Boundedness Principle

  1. Pingback: Camtasia Studio and Echo360 | Explaining mathematics

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