The course will cover the fundamentals of linear Functional Analysis and will include (not limited to) the following topics:
- Abstract Banach and Hilbert spaces, The Hahn-Banach Theorems, The Uniform Boundedness Principle and Closed Graph Theorems, Weak Topologies, Reflexive Spaces, Separable Spaces, Uniform Convexity, Linear Operators, Banach and Hilbert adjoint, Compact Operators, Introduction to Spectral Theory for Linear Operators.
Functional Analysis, Sobolev Spaces and Partial Differential Equations, by Haïm Brézis, ISBN 978-0-387-70913-0
Math 501, Math 502