Functional Analysis

September 2004— February 2005

Timetable

Chapter 1  Topological Vector Spaces

Lecture 1  Review on some basic concepts

Lecture 2  Separation and Linear Mappings

    Review    (Lecture 1 and Lecture 2)

Lecture 3  Finite-Dimensional Spaces

Lecture 4  Metrization

Lecture 5 Boundedness, Continuity, $L^p, 0<p<1$

Lecture 6   Seminorms and Local Convexity

Lecture 7  Quotient Spaces

Lecture 8  Examples and Exercises

　

Chapter 2   Completeness

Lecture 1  Baire Category, Banach-Steinhaus Theorem

Lecture 2  Open Mapping Theorem

Lecture 3  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  Compact Convex Sets

Lecture 6  Extreme points

Lecture 7  Vector -Valued Integration

Lecture 8  Holomorphic Functions

　

Chapter 4  Duality in Banach Spaces

Lecture 1  The Normed Dual of a Normed Space

Lecture 2  The Normed Dual of a Normed Space (continued)

Lecture 3  The Adjoint Operator

Lecture 4  Compact Operators

Lecture 5  Compact Operators (continued)

　

Chapter 5  Some Applications

　

Chapter 10  Banach Algebras

Lecture 1  Definition, Homomorphisms

Lecture 2  Basic Properties of Spectra

 Lecture 3   Symbolic Calculus

Lecture 4  The Group G(A),  Invariant Subspaces

　

Chapter 11  Commutative Banach Algebra

Lecture 1   Ideals and Homomorphisms

Lecture 2   Gelfand Transforms

Lecture 3   Involutions

Notice on the Examination

Homework

Chapter 1 ;       Chapter 2;      Chapter 3;    Chapter 4.   Review

　

Seminar 

Seminar (timetable)