Chapter 1: Banach Spaces
- Normed linear spaces
- Lp spaces and Hardy Spaces
- Linear operators
Chapter 2: The Basic Principles
- The Hahn-Banach Theorem
- The Uniform Boundedness Principle
- The Open Mapping and Closed Graph Theorems
Chapter 3: Hilbert Spaces
- Inner product spaces
- Adjoint operators
- Weak convergence
- The Spectral Theorem
Chapter 4: Methods of Optimization
- Maximizing vectors
- Pseudoinverse operators
- Optimization of functionals
- Constrained optimization