This course will cover fundamental topics of linear functional analysis. Topics include (but not limited to): The Hahn-Banach Theorems, The Uniform Boundedness Principle and Closed Graph Theorems, Weak Topologies, Reflexive Spaces, Separable Spaces, Uniform Convexity, Hilbert Spaces, Compact Operators, Spectral Theory for Compact and Selfadjoint Operators.
Functional Analysis, Sobolev Spaces and Partial Differential Equations, by Haïm Brézis
Math 501, Math 502