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David Penneys
Assistant Professor of Mathematics at The Ohio State University Office: Room 752 Math Tower Office hours: Friday 11:30-12:30 or by appointment Email: penneys (dot) 2 (at) osu (dot) edu |
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MATH 7211 and 7212: Functional Analysis
Files
Here you can find the syllabi, a TeX homework template, and the problem list. Here are the notes from 7211 from Autumn 2017.
Here you can find the syllabi, a TeX homework template, and the problem list. Here are the notes from 7211 from Autumn 2017.
- Notes on topological vector spaces
- Notes on dual spaces
- Notes on compact operators
- Notes on Fredholm operators
- Notes on Banach algebras
- Notes on C*-algebras
- Notes on basic von Neumann algebras and the spectral theorem
- Notes on projections and factors
- Notes on crossed products
- Notes on amenability, the Haagerup property, and property (T)
- Notes on equivalence relations and orbit equivalence
- Vaughan Jones' notes on von Neumann algebras
- Anantharaman, Claire and Popa, Sorin. An introduction to II_1 factors
- Jesse Peterson's notes on operator algebras, ergodic theory, etc.
- Jesse Peterson's notes on von Neumann algebras
- Dana P. Williams' notes on the spectral theorem
Announcements for 7212
2018/4/16, 10:05
Homework 14
The final assignment consists of problems 114, 115, 116, and it is due April 23.
2018/4/7, 17:19
Homework 13
Problems 109, 112, and one of 110 or 111 are due April 16.
2018/4/2, 9:01
Homework 12
Problems 106, 107, 108 are due April 9.
2018/3/28, 10:05
Homework 11
Problems 103, 104, 105 are due April 2.
2018/3/19, 15:43
Homework 10
Problems 100, 101, 102 are due March 26.
2018/3/5, 11:47
Homework 9
Problems 93, 95, 96, 97 are due March 19.
2018/2/22, 13:01
Homework 8
Problems 89, 91, 92 are due March 5.
2018/2/20, 15:07
Homework 7
Problems 84, 86, 87, 88 are due February 26.
2018/2/7, 10:03
Homework 6
Problems 81, 82, and 83 are due February 19.
2018/2/1, 20:43
Homework 5
Problems 76, 77, 78, and 79 are due February 12.
2018/1/29, 13:48
Homework 4
Problems 73, 74, and 75 are due February 5.
2018/1/22, 10:06
Homework 3
Problems 70, 71, and 72 are due January 29.
2018/1/11, 9:25
Homework 2
Problems 67 and 68 are due January 22.
2018/1/10, 19:15
Typo in problem 64
I've editted it. Hopefully it's correct now.
2018/1/8, 12:45
Tentative 7212 syllabus posted
Please find the tentative syllabus posted above.
2018/1/3, 12:15
Homework 1
Problems 62, 63, 64, and 65 are due Wednesday January 17. They would be due Monday January 15, but that is MLK day. Homework 2 will only consist of 2 problems, but will still be due January 22. You may use any statements from last semester without proof.
2018/1/2, 10:19
7212 syllabus
I will soon post the syllabus for 7212.
2018/4/16, 10:05
Homework 14
The final assignment consists of problems 114, 115, 116, and it is due April 23.
2018/4/7, 17:19
Homework 13
Problems 109, 112, and one of 110 or 111 are due April 16.
2018/4/2, 9:01
Homework 12
Problems 106, 107, 108 are due April 9.
2018/3/28, 10:05
Homework 11
Problems 103, 104, 105 are due April 2.
2018/3/19, 15:43
Homework 10
Problems 100, 101, 102 are due March 26.
2018/3/5, 11:47
Homework 9
Problems 93, 95, 96, 97 are due March 19.
2018/2/22, 13:01
Homework 8
Problems 89, 91, 92 are due March 5.
2018/2/20, 15:07
Homework 7
Problems 84, 86, 87, 88 are due February 26.
2018/2/7, 10:03
Homework 6
Problems 81, 82, and 83 are due February 19.
2018/2/1, 20:43
Homework 5
Problems 76, 77, 78, and 79 are due February 12.
2018/1/29, 13:48
Homework 4
Problems 73, 74, and 75 are due February 5.
2018/1/22, 10:06
Homework 3
Problems 70, 71, and 72 are due January 29.
2018/1/11, 9:25
Homework 2
Problems 67 and 68 are due January 22.
2018/1/10, 19:15
Typo in problem 64
I've editted it. Hopefully it's correct now.
2018/1/8, 12:45
Tentative 7212 syllabus posted
Please find the tentative syllabus posted above.
2018/1/3, 12:15
Homework 1
Problems 62, 63, 64, and 65 are due Wednesday January 17. They would be due Monday January 15, but that is MLK day. Homework 2 will only consist of 2 problems, but will still be due January 22. You may use any statements from last semester without proof.
2018/1/2, 10:19
7212 syllabus
I will soon post the syllabus for 7212.
Announcements for 7211
2017/11/15, 12:19
Homework 13 error!
I needed to re-order the problems for HW 13, since you might want to use that the sum of spectrally positive operators is spectrally positive in order to show that a spectrally positive operator is positive (of the form a*a). Thanks to Sam for pointing this out. So Problems 49, 50, 51, and 53 are due Monday.
2017/11/8, 13:26
Homework 15
The final homework consists of Problems 59, 60, and 61 and is due Monday 12/4. (Warning: numbers subject to change...)
2017/11/8, 13:26
Homework 14
Problems 54 and 55 are due Monday 11/27. (Warning: numbers subject to change...)
2017/11/6, 10:00
Homework 13
Problems 49, 50, 51, and 53 are due Monday 11/20.
2017/11/6, 10:00
Homework 12
Problems 45, 46, and one of 47 or 48 are due Monday 11/13.
2017/10/23, 12:38
Homework 11
Problems 40, 41, 42, and 43 are due Monday 11/6.
2017/10/23, 8:16
Handwritten notes on Banach algebras
I've posted some handwritten notes on Banach algebras up through the holomorphic functional calculus and dependence of the spectrum on the algebra. I'll update them again after we cover the Gelfand theory. Additional sources for this material include John B. Conway's A Course in Functional Analysis.
2017/10/18, 14:42
Homework 10
Problems 36, 38, and 39 are due Monday 10/30.
2017/10/16, 13:21
Homework 9
Problems 33, 34, and 35 are due Monday 10/23.
2017/10/6, 18:30
Notes on Fredholm operators
I thought the lecture from 10/6 could have gone a bit better, so I wrote up some notes. You can find the link above.
2017/10/4, 9:52
Homework 8
Problems 29, 30, and 31 are due Monday 10/16.
2017/9/29, 15:51
Homework 7
This homework assignment consists of one of Problem 21 or 22, together with one of Problem 23 or 24. I will only grade one of each, so if you do more, please specify which I should grade. Solutions are due Monday 10/9.
2017/9/24, 11:22
Homework 6
Problems 16, 17, 18, 19, and 20 from the problem list are due Monday 10/2.
2017/9/13, 16:54
Homework 5
Problems 12 and 13 from the problem list are due Monday 9/25.
2017/9/9, 13:26
Homework 4
Problems 9, 10, and 11 from the problem list are due Monday 9/18.
2017/9/5, 10:25
Homework 3
Problems 5, 6, and 7 from the problem list are due Monday 9/11.
2017/8/31, 1:10
Homework 2
Problems 3 and 4 from the problem list are due Monday 9/4.
2017/8/23, 14:42
Homework 1
Problems 1 and 2 from the problem list are due Monday 8/28.
2017/8/23, 14:42
Problem list posted
The problem list has been posted in the files section.
2017/8/14, 11:00
Tentative syllabus posted
You can find it above in the files section.
2017/11/15, 12:19
Homework 13 error!
I needed to re-order the problems for HW 13, since you might want to use that the sum of spectrally positive operators is spectrally positive in order to show that a spectrally positive operator is positive (of the form a*a). Thanks to Sam for pointing this out. So Problems 49, 50, 51, and 53 are due Monday.
2017/11/8, 13:26
Homework 15
The final homework consists of Problems 59, 60, and 61 and is due Monday 12/4. (Warning: numbers subject to change...)
2017/11/8, 13:26
Homework 14
Problems 54 and 55 are due Monday 11/27. (Warning: numbers subject to change...)
2017/11/6, 10:00
Homework 13
Problems 49, 50, 51, and 53 are due Monday 11/20.
2017/11/6, 10:00
Homework 12
Problems 45, 46, and one of 47 or 48 are due Monday 11/13.
2017/10/23, 12:38
Homework 11
Problems 40, 41, 42, and 43 are due Monday 11/6.
2017/10/23, 8:16
Handwritten notes on Banach algebras
I've posted some handwritten notes on Banach algebras up through the holomorphic functional calculus and dependence of the spectrum on the algebra. I'll update them again after we cover the Gelfand theory. Additional sources for this material include John B. Conway's A Course in Functional Analysis.
2017/10/18, 14:42
Homework 10
Problems 36, 38, and 39 are due Monday 10/30.
2017/10/16, 13:21
Homework 9
Problems 33, 34, and 35 are due Monday 10/23.
2017/10/6, 18:30
Notes on Fredholm operators
I thought the lecture from 10/6 could have gone a bit better, so I wrote up some notes. You can find the link above.
2017/10/4, 9:52
Homework 8
Problems 29, 30, and 31 are due Monday 10/16.
2017/9/29, 15:51
Homework 7
This homework assignment consists of one of Problem 21 or 22, together with one of Problem 23 or 24. I will only grade one of each, so if you do more, please specify which I should grade. Solutions are due Monday 10/9.
2017/9/24, 11:22
Homework 6
Problems 16, 17, 18, 19, and 20 from the problem list are due Monday 10/2.
2017/9/13, 16:54
Homework 5
Problems 12 and 13 from the problem list are due Monday 9/25.
2017/9/9, 13:26
Homework 4
Problems 9, 10, and 11 from the problem list are due Monday 9/18.
2017/9/5, 10:25
Homework 3
Problems 5, 6, and 7 from the problem list are due Monday 9/11.
2017/8/31, 1:10
Homework 2
Problems 3 and 4 from the problem list are due Monday 9/4.
2017/8/23, 14:42
Homework 1
Problems 1 and 2 from the problem list are due Monday 8/28.
2017/8/23, 14:42
Problem list posted
The problem list has been posted in the files section.
2017/8/14, 11:00
Tentative syllabus posted
You can find it above in the files section.
last modified: 2018/4/16