### MATH 418 - Honors Real Variables, II and MATH 516 - Linear Analysis

### Instructor

### Office hours

### Content

- classical Banach spaces;

- Hahn-Banach, open mapping, and closed graph theorems;

- Hilbert spaces and orthonormal bases;

- elements of spectral theory, spectra of compact operators, and the
spectral theorem for compact self-adjoint operators.

### Textbooks

I won't require any particular textbook, but you may find the following
ones useful to to look into:
- K. Saxe,
*Beginning Functional Analysis*. Springer Verlag,
2002.

- B. Bollobás,
*Linear Analysis*, Second Edition. Cambridge University
Press, 1999.

- J. B. Conway,
*A Course in Functional Analysis*. Springer Verlag, 1985.

### Grading

The mark will be based on weekly homework assignments (30%), an
in-class-midterm on October 17 (20%), and a final (50%). A total mark of 50% will yield a grade of D or better, and a total mark of 90% will yield a grade
of A (or better). Prior to both the midterm and the final, a practice midterm/final will be made available.

Last update: 1/09/15.