Hilbert and Banach spaces

Primary reference

1. Functional Analysis - Peter D. Lax.

Other useful references

1. Functional Analysis - Reed and Simon.

2. Functional Analysis - Rudin.

3. Essential results of functional analysis - Zimmer

Topics for the Fall (528A)

• Linear spaces, linear maps and extensions.

• Normed linear spaces, completeness, Hilbert and Banach spaces.

• Duality and applications; weak convergence.

• Convexity.

• Bounded and Compact linear operators.

Grading policy, etc.

• Homework will be assigned regularly, roughly once every two-three weeks.

• You have the option of working on a project and presenting your work, or a take home final. If you choose to work on a project, that work can be extended in the spring for Math 528B.

• Here is a list of potential projects. You can pick one of these topics or come talk to me if you have some ideas you would like to investigate.

Homework

Homework 1

Homework 2

Homework 3

Homework 4