Math 421/510 - Functional Analysis - Spring 2018
Instructor: Malabika Pramanik
Office: 214 Mathematics Building
E-mail: malabika at math dot ubc dot ca
Lectures: Tuesday and Thursday 11:00 AM to 12:30 PM in Room 203 of Mathematics Building.
Office hours: Tuesday 10-11, Thursday 2-3 or by appointment.
Marker/TA : Tongou (Thomas) Yang
E-mail : toyang at math dot ubc dot ca
- Quiz 1 held at the end of class on Thursday, January 11. Solution
- Quiz 2 held at the end of class on Thursday, January 18. Solution
- Quiz 3 held at the end of class on Thursday, January 25. Solution
- Quiz 4 held at the end of class on Thursday, February 8. Solution
Weeks 5 and 6
- Weeks 1 and 2
- Practice problems: Chapter 5, Section 5.1, Exercises 1-16 of the textbook. These are not to be turned in.
- Homework set 1: Exercises 6, 8, 9, 13. (due on Tuesday Jan 23 at the beginning of lecture) Homework 1 Solution
- Weeks 3 and 4
- Practice problems: Chapter 5, Section 5.2, Exercises 17-26 of the textbook. These are not to be turned in.
- Homework set 2 (due on Tuesday Feb 6 at the beginning of lecture)
- Homework 2 Solution
- Practice problems: Chapter 5, Section 5.5, Exercises 54-67 of the textbook. These are not to be turned in.
- Homework set 3: Exercises 55, 56, 57, 58, 62. (due on Tuesday Feb 27 at the beginning of lecture)
Week-by-week course outline
This section contains a summary of the material covered in class, arranged by week. The treatment of these topics in lecture may vary somewhat from that of the text. Please stay tuned for possible changes.
- Week 1:
- Linear spaces
- Examples of infinite dimensional linear spaces
- Week 2:
- Normed linear spaces
- Topology induced by a norm
- Finite-dimensional normed spaces
- Week 3:
- Separable spaces: examples and non-examples
- Non-compactness of the unit ball in infinite-dimensional normed spaces
- Hamel and Schauder bases
- Week 4:
- Hahn-Banach theorem: the real case
- An application of Hahn-Banach: the hyperplane separation theorem
- Week 5:
- The Minkowski functional
- Hahn-Banach theorem: the complex version
- Hilbert spaces
- Closest point to a convex set in a Hilbert space
- Week 6:
- Orthogonal projections and orthogonal complements
- Orthonormal bases
- Bounded linear functionals on Hilbert spaces
- Riesz-Frechet representation theorem on Hilbert spaces