Functional Analysis

September 2005— January 2006

Timetable

Chapter 1  Topological Vector Spaces

Lecture 1 Review on some basic concepts (I)

Lecture 2 Review on some basic concepts (II)

Lecture 3 Separation Properties

Lecture 4 Further properties of a TVS, Linear Mappings

Lecture 5 Finite-Dimensional Spaces

Lecture 6 Metrization

Lecture 7 Boundedness, Continuity

Lecture 8 $L^p, 0<p<1$

　 Lecture 9 Seminorms and Local Convexity

Lecture 10 Quotient Spaces

Lecture 11 Examples and Exercises

Chapter 2   Completeness

Lecture 1 Baire Category, Banach-Steinhaus Theorem

Lecture 2 Banach-Steinhaus Theorem

Lecture 3 The Open Mapping Theorem，The Inverse Mapping Theorem

The Closed Graph Theorem, Bilinear Mappings

Chapter 3  Convexity

Lecture 1 Hahn-Banach Theorems, Extension and Separation

Lecture 2 Weak Topologies

Lecture 3 Weak Topologies and Compact Convex Sets

 Lecture 4 Compact Convex Sets

Lecture 5 Vector -Valued Integration

Lecture 6 Holomorphic Functions

Chapter 4  Duality in Banach Spaces

Lecture 1 The Normed Dual of a Normed Space

Lecture 2 The Adjoint Operator

Lecture 3 Compact Operators

Lecture 4 Compact Operators (continued)

Chapter 5  Some Applications

Seminars