Functional Analysis
September
2006— January 2007
Chapter 1 Topological Vector Spaces
Lecture 1 Review on some basic concepts
Lecture 2 Separation and Linear Mappings
Lecture 3 Finite-Dimensional Spaces
Lecture 4
Boundedness,
Continuity
Lecture 5 Seminorms and Local Convexity, Quotient Spaces
Lecture 6
Basic review, Examples and Exercises
Chapter 2 Completeness
Lecture 1 Baire Category, Banach-Steinhaus Theorem
Lecture 2
Banach-Steinhaus Theorem
Lecture 3 Theorems of Open Mapping, Inverse
Mapping, Closed Graph; and Bilinear Mappings
Chapter 3 Convexity
Lecture 1 Hahn-Banach Theorems, Extension and Separation
Lecture 2 Weak and Weak* Topologies
Lecture 3 Compact Convex Sets and Vector -Valued Integration
Lecture 4 Holomorphic Functions
Chapter 4 Duality in Banach Spaces
Lecture 1 The Normed Dual and Adjoint
Lecture 2 Compact Operators
Chapter
5 Some Applications