Functional Analysis(I)- Course Video

Chapter 3 Weak Topologies, Reflexive Spaces, Separable Spaces, and Uniform Convexity
- 3.1 Weak Topologies Preliminaries
- 3.2 Weak Topology and Weak Convergence
- 3.3 Weak Topologies, Convex Set, and Linear Operators
- 3.4 The Weak* Topologies sigma(E*,E)
- 3.5 Reflexive Spaces
- 3.6 Separable Spaces
- 3.7 Uniformly Convex Spaces
- Review Session
- Exercises
Chapter 4 L^p Spaces
- 4.2 Definition and Elementary Properties of L^p Spaces
- 4.3 Reflexivity, Separability, and Dual of L^p
- 4.4 Convolution and regularization
- 4.5 Criterion for Strong Compactness in L^p
- Review Session
- Exercises
Chapter 5 Hilbert Spaces
- 5.1 Definitions and Elementary Properties, Projections onto a Closed Convex Set
- 5.2 The Dual Space of a Hilbert Space
- 5.3 The Theorems of Stampacchia and Lax Milgram
- 5.4 Hilbert Sums, Orthonormal Bases
- Review Session
- Exercises
Chapter 6 Compact Operators, Spectral Decomposition of Self Adjoint Compact Operators
- 6.1 Definitions, Elementary Properties, and Adjoint
- 6.2 The Riesz-Fredholm Theory
- 6.3 The Spectrum of a Compact Operator
- 6.4 Spectral Decomposition of Self-Adjoint Compact Operators
- Review Session
- Exercises
Final Review Session