Functional Analysis

Lecture 8 - The proof of Tychonoff's theorem

Oct. 4, 2010

0:44:55

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Lecture 1 - Functional Analysis, Introductory material on totally ordered sets and partially ordered sets

July 9, 2010

0:35:09

Lecture 1 - ( for iPod) Functional Analysis, Introductory material on totally ordered sets and partially ordered sets

Nov. 26, 2010

Lecture 2 - Complete metric spaces

0:41:29

Lecture 2 - (for iPod) Complete metric spaces

Lecture 3 - revision of Metric and Topological Spaces

July 14, 2010

0:44:32

Lecture 3 - (for iPod) revision of Metric and Topological Spaces

Lecture 4 - Complete metric spaces - printed slides 7-9

July 16, 2010

Lecture 4 - (for iPod) Complete metric spaces - printed slides 7-9

0:45:12

Lecture 5a - Complete metric spaces - printed slide 9 to end of Chapter 1

Aug. 6, 2010

0:32:30

Lecture 5a - (for iPod) Complete metric spaces - printed slide 9 to end of Chapter 1

Lecture 5b - Chapter 2: Infinite products and Tychonoff’s theorem, printed slides 13-14

Aug. 24, 2010

0:10:43

Lecture 5b - (for iPod) Chapter 2: Infinite products and Tychonoff’s theorem, printed slides 13-14

Lecture 6a - discussion session

Sept. 1, 2010

0:12:22

Lecture 6a - (for iPod) discussion session

Lecture 6b - discussion session part b

Oct. 25, 2010

0:32:40

Lecture 6b (for iPod) - discussion session part b

Lecture 7 - Infinite products and Tychonoff's theorem

0:48:05

Lecture 7 - (for iPod) Infinite products and Tychonoff's theorem

Lecture 8 (for iPod) - The proof of Tychonoff's theorem

Lecture 9a - Infinite products and Tychonoff's theorem - printed slide 26 to end of chapter

0:26:22

Lecture 9a (for iPod) - Infinite products and Tychonoff's theorem - printed slide 26 to end of chapter

Lecture 9b - Normed spaces and Banach spaces - printed slides 28-31

0:13:01

Lecture 9b - (for iPod) - Normed spaces and Banach spaces - printed slides 28-31

Lecture 10 - Normed spaces and Banach spaces - printed slides 31-34

Oct. 29, 2010

0:47:11

Lecture 10 - (for iPod) Normed spaces and Banach spaces - printed slides 31-34

Lecture 11a - printed slides 33-34 continued, completeness of the uniform norm

0:26:40

Lecture 11a - (for iPod) printed slides 33-34 continued, completeness of the uniform norm

Lecture 11b - Interlude on pointwise convergence and uniform convergence

0:23:19

Lecture 11b - (for iPod) Interlude on pointwise convergence and uniform convergence

Lecture 12 - Normed spaces and Banach spaces - printed slides 33-34 concluded, and printed slides 35-37

Jan. 10, 2011

0:43:19

Lecture 12 - (for iPod) Normed spaces and Banach spaces - printed slides 33-34 concluded, and printed slides 35-37

Lecture 13a - Normed spaces and Banach spaces - final discussion of Section 3.1

0:09:01

Lecture 13a - (for iPod) Normed spaces and Banach spaces - final discussion of Section 3.1

Lecture 13b - Equivalence of norms - whole section discussed, including discussion of facts needed to prove Theorem 3.8

0:31:44

Lecture 13b - (for iPod) Equivalence of norms - whole section discussed, including discussion of facts needed to prove Theorem 3.8

Lecture 14a - Equivalence of norms - recap of preliminary discussion relating to Theorem 3.8

Feb. 1, 2011

0:03:48

Lecture 14a - (for iPod) Equivalence of norms - recap of preliminary discussion relating to Theorem 3.8

Lecture 14b - Equivalence of norms - "conclusion" of Section 3.2, including the proofs of Theorems 3.8 and 3.10

March 17, 2011

0:47:26

Lecture 14b - (for iPod) Equivalence of norms - "conclusion" of Section 3.2, including the proofs of Theorems 3.8 and 3.10

Lecture 15a - Equivalence of norms - final discussion of Section 3.2

April 1, 2011

0:10:07

Lecture 15a - (for iPod) Equivalence of norms - final discussion of Section 3.2

Lecture 15b - Linear maps - Section 3.3, printed slides 41-43

0:35:04

Lecture 15b - (for iPod) Linear maps - Section 3.3, printed slides 41-43

Lecture 16a - (for iPod) Linear maps - Conclusion of Section 3.3 including recap, & printed slide 44.

April 16, 2011

0:24:42

Lecture 16a - Linear maps - Conclusion of Section 3.3 including recap, & printed slide 44

Lecture 16b - Sequence spaces - Section 3.4, printed slides 45-48

0:17:44

Lecture 16b - (for iPod) Sequence spaces - Section 3.4, printed slides 45-48

Lecture 17 - Sequence spaces - Recap of Section 3.4 and proof of part of Theorem 3.15

April 27, 2011

0:46:30

Lecture 17 - (for iPod) Sequence spaces - Recap of Section 3.4 and proof of part of Theorem 3.15

Lecture 18a - Sequence spaces - Conclusion of Section 3.4

0:36:00

Lecture 18a - (for iPod) Sequence spaces - Conclusion of Section 3.4

Lecture 18b - Isomorphisms - Introduction to Section 3.5: printed slides 49-51

0:07:07

Lecture 18b - (for iPod) Isomorphisms - Introduction to Section 3.5: printed slides 49-51

Lecture 19a - Isomorphisms - Conclusion of Section 3.5: printed slides 51-54

May 6, 2011

0:24:49

Lecture 19a - (for iPod) Isomorphisms - Conclusion of Section 3.5: printed slides 51-54

Lecture 19b - Sums and quotients of vector spaces - Section 3.6, printed slides 55-57

0:17:11

Lecture 19b - (for iPod) Sums and quotients of vector spaces - Section 3.6, printed slides 55-57

Lecture 20a - Sums and quotients of vector spaces - Conclusion of Section 3.6, printed slides 57-60

June 10, 2011

0:22:06

Lecture 20a - (for iPod) Sums and quotients of vector spaces - Conclusion of Section 3.6, printed slides 57-60

Lecture 20b - Section 3.7: Dual spaces - Section 3.7, printed slides 61-64

0:22:40

Lecture 20b - (for iPod) Section 3.7: Dual spaces - Section 3.7, printed slides 61-64

Lecture 21 - Duals and Double Duals - Section 3.7, printed slides 64-65

Jan. 23, 2012

0:35:37

Lecture 21 - (for iPod) Duals and Double Duals - Section 3.7, printed slides 64-65

Lecture 22 - Conclusion of Section 3.7 and brief introduction to Section 3.8

Jan. 28, 2012

0:41:19

Lecture 22 - (for iPod) Conclusion of Section 3.7 and brief introduction to Section 3.8

Lecture 23 - Extensions of linear maps

0:45:53

Lecture 23 - (for iPod) Extensions of linear maps

Lecture 24 - Completions, quotients and Riesz's Lemma

0:40:44

Lecture 24 - (for iPod) Completions, quotients and Riesz's Lemma

Lecture 25 - The Weak-* Topology and the Banach-Alaoglu Theorem

Jan. 29, 2012

0:42:57

Lecture 25 - (for iPod) The Weak-* Topology and the Banach-Alaoglu Theorem

Lecture 26 - Open Mappings and their Applications

0:38:29

Lecture 26 - (for iPod) Open Mappings and their Applications

Jan. 30, 2012

Lecture 27 - The open mapping lemma

0:40:00

Lecture 27 - (for iPod) The open mapping lemma

Lecture 28 - part a - Recap concerning convex sets which are symmetric about 0

0:02:03

Lecture 28 - part a - (for iPod) Recap concerning convex sets which are symmetric about 0

Lecture 28 - part b - Chapter 5, printed slides 102-108, Proof of Open Mapping Theorem

Feb. 13, 2012

0:44:28

Lecture 28 - part b (for iPod) - Chapter 5, printed slides 102-108, Proof of Open Mapping Theorem

Lecture 32 (for iPod) - Discussion session on measure theory

March 16, 2012

0:46:15

Lecture 29 part a - Recap, and proof of the Closed Graph Theorem

0:18:14

Lecture 29 part a - (for iPod) Recap, and proof of the Closed Graph Theorem

Lecture 29 part b - The Uniform Boundedness Principle/Banach-Steinhaus

0:21:39

Lecture 29 part b (for iPod) - The Uniform Boundedness Principle/Banach-Steinhaus

Lecture 30 - Commutative Banach Algebras, printed slides 1-19

0:47:32

Lecture 30 (for iPod)- Commutative Banach Algebras, printed slides 1-19

Lecture 31 - Commutative Banach Algebras, printed slides 19-29

Feb. 22, 2012

0:46:14

Lecture 31 (for iPod) - Commutative Banach Algebras, printed slides 19-29

Lecture 32 - Discussion session on measure theory

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