Syllabus

Text: R. E. Edwards, Functional Analysis. Theory and Applications, Holr, Rinehart and Winston, New York, 1965, reprinted by Dover Publications Inc.

• Review of metric spaces
• Review of topological spaces
• Introduction to normed spaces and inner product spaces.
• Hilbert space and orthogonal projection theorem
• Topological vector spaces, chapter 1
• Seminorms and locally convex spaces, chapter 1
• Hahn-Banach theorem, chapter 2
• Fixed-point theorems, Schauder fp theorem, chapter 3
• Distribution theory, chapter 5
• Open mapping and closed graph theorems, chapter 6
• Banach-Steinhaus theorem, chapter 7
• Duality. Compatible topologies, chapter 8
• Krein-Milman theorem, chapter 10

We are unlikely to cover everything plus some applications! The exact material covered will depend on my energy and the class's interest. Some material will be covered in less generality than in the text.

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