Functional Analysis

On this page I give links to the complete set of (streaming video) screencasts from the 2009-10 edition of my fourth-year module G14FUN Functional Analysis (University of Nottingham).

New! The complete set of videos, lecture notes, question sheets and solutions, etc., can now be viewed or downloaded (1.9 Gb) from

http://unow.nottingham.ac.uk/resources/resource.aspx?hid=c9eec1dc-8c27-9949-dc16-2728edf6c994

as part of the University of Nottingham Open Courseware Repository U-NoW (http://unow.nottingham.ac.uk).

Similarly, the 2006-7 and 2007-8 versions of this module, including the printed notes and slides and audio recordings, and many other module materials, are available from

http://unow.nottingham.ac.uk/resources/resource.aspx?hid=bd32d53b-3c12-ac19-176b-d9e112731951

In the screencasts below, the quality of the picture-in-picture video of me in the corner was mostly poor for the first few lectures, but improved a lot once I started using a desk lamp for additional illumination from lecture 8 onwards.

• Lecture 1 (introductory material on totally ordered sets and partially ordered sets)
• Lecture 2 (Chapter 1: Complete metric spaces, printed slides 1-8)
• Lecture 3 (revision of Metric and Topological Spaces)
• Lecture 4 (printed slides 7-9)
• Lecture 5, part a (printed slide 9 to end of Chapter 1)
• Lecture 5, part b (Chapter 2: Infinite products and Tychonoff’s theorem, printed slides 13-14)
• Lecture 6 (YouTube edition): Part a, Part b (discussion session on totally ordered sets and partially ordered sets)
• Lecture 7 (printed slides 13-25)
• Lecture 8 (printed slides 20-27)
• Lecture 9, part a (printed slide 26 to end of Chapter2)
• Lecture 9, part b (Section 3.1:  Normed spaces and Banach spaces, printed slides 28-31)
• Lecture 10 (printed slides 31-34)
• Lecture 11, part a (printed slides 33-34 continued, completeness of the uniform norm)
• Lecture 11, part b (Interlude on pointwise convergence and uniform convergence)
• Lecture 12 (printed slides 33-34 concluded, and printed slides 35-37)
• Lecture 13, part a (final discussion of Section 3.1)
• Lecture 13, part b (Section 3.2: Equivalence of norms, whole of Section 3.2 discussed, including discussion of facts needed to prove Theorem 3.8)
• Lecture 14, part a (recap of preliminary discussion relating to Theorem 3.8, laptop running on batteries)
• Lecture 14, part b (“conclusion” of Section 3.2, including the proofs of Theorems 3.8 and 3.10)
• Lecture 15, part a (final discussion of Section 3.2).
• Lecture 15, part b (Section 3.3: Linear maps, printed slides 41-43)
• Lecture 16, part a (Conclusion of Section 3.3 including recap, printed slide 44, connections with Lipschitz continuity)
• Lecture 16, part b (Section 3.4: Sequence spaces,  printed slides 45-48)
• Lecture 17 (Recap of Section 3.4 and proof of part of Theorem 3.15)
• Lecture 18, part a (Conclusion of Section 3.4)
• Lecture 18, part b (Section 3.5: Isomorphisms, printed slides 49-51)
• Lecture 19, part a (Conclusion of Section 3.5: printed slides 51-54)
• Lecture 19, part b (Section 3.6: Sums and quotients of vector spaces, printed slides 55-57)
• Lecture 20, part a (Conclusion of Section 3.6, printed slides 57-60)
• Lecture 20, part b (Section 3.7: Dual spaces, printed slides 61-64)
• Lecture 21 (Section 3.7, printed slides 64-65)
• Lecture 22 (Conclusion of Section 3.7 and brief introduction to Section 3.8).
• Lecture 23 (All of Section 3.8, Extensions of linear maps)
• Lecture 24 (All of Section 3.9, Completions, quotients and Riesz’s Lemma)
• Lecture 25 (All of Chapter 4, The Weak-* Topology and the Banach-Alaoglu Theorem)
• Lecture 26 (Chapter 5: Open Mappings and their Applications, printed slides 93-96)
• Lecture 27 (Chapter 5, printed slides 97-102)
• Lecture 28, part a (Recap concerning convex sets which are symmetric about 0, laptop running on battery power)
• Lecture 28, part b (Chapter 5, printed slides 102-108, note a ‘typo’ in the proof of Lemma 5.8 where one A should be an E)
• Lecture 29, part a (Recap, and proof of the Closed Graph Theorem)
• Lecture 29, part b (All of Chapter 6, The Uniform Boundedness Principle/Banach-Steinhaus)
• Lecture 30 (Commutative Banach Algebras, printed slides 1-19)
• Lecture 31 (Commutative Banach Algebras, printed slides 19-29)
• Lecture 32 (Discussion session on measure theory material)