Linear Analysis I

Math 675-001

Fall 2017


The following table contains the schedule for the course. It will basically cover Chapters 2, 4, 5, and 6 of the textbook, as well as additional material. This page will be updated regularly throughout the semester.

Week Date Sections
I. Introduction
1 08/29     1. Superposition principle
08/31     2. Solvability conditions
II. Metric Spaces
2 09/05     1. Basic definitions 5.1
09/07     2. Convergence and continuity 5.2, 6.2
3 09/12     3. Topological properties 6.1, 6.4, 6.5, 6.6
09/14     4. Completeness 7.1, 7.2, 7.4
4 09/19     No class!
09/21     5. Separable metric spaces 6.3
    6. Completion of a metric space 7.4
5 09/26     No class!
09/28     7. Compactness 10.1, 10.2, 10.3, 10.4
III. Linear Spaces
6 10/03     1. Linear spaces 13.1, 13.2, 13.3
10/05     2. Frechet spaces 17.1, 17.2
    3. Banach spaces 15.1, 15.2
7 10/10     No class! (Columbus Day)
10/12     4. Finite-dimensional Banach spaces
8 10/17     5. Compactness of the unit sphere
    6. Hilbert spaces 16.1, 16.2, 16.8, 16.9
10/19     7. Orthonormal sets 16.3, 16.4, 16.5, 16.6
9 10/24     8. Orthogonal projections 16.7
10/26     9. Superposition principle revisited
IV. Linear Functionals
10 10/31     1. Continuous linear operators 18.1, 18.2, 22.1, 22.2
11/02     Midterm Exam
11 11/07     2. The Banach algebra L(X,X) 22.3
    3. Dual spaces 19.1, 19.2
11/09     4. The Hahn-Banach theorem 14.4, 18.3
12 11/14     5. Reflexive spaces 19.4
V. Linear Operators
11/16     1. Inverse operators 23.1
    2. Adjoint operators 23.2, 23.3
13 11/21     No class!
11/23     No class! (Thanksgiving)
14 11/28     3. Solvability conditions
11/30     4. Spectrum and resolvent 23.4
15 12/05     5. Completely continuous operators 24.1, 24.2
12/07     6. The Fredholm-Riesz-Schauder theory 24.3
16 12/14     Final Exam, 4:30-7:15pm

In addition to the textbook, you might find the following books useful for supplementary reading:


Thomas Wanner, October 20, 2017.