R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Student Seminar on Functional Analysis
Hsiang-Tzu Chiu (NCTS)
Notice：
If one topic takes longer time, the rest of the schedule can be pushed back; if one topic movesaster, we may start the next topic earlier. The lecture content will generally follow the schedule, with additional materials and supplements provided.
Shedule (Every Friday from September 5)：
Week 1 (9/5)
The Analytic Form of the Hahn-Banach Theorem
The Geometric Form of the Hahn-Banach Theorem
Week 2 (9/12)
The Bidual and Orthogonality Relations
A Brief Introduction to Convex Analysis (I)
Week 3 (9/19)
A Brief Introduction to Convex Analysis (II)
The Baire Category Theorem
Week 4 (9/26)
The Uniform Boundedness Principle
The Open Mapping Theorem and the Closed Graph Theorem
Week 5 (10/3)
Complementary Subspaces
Orthogonality Revisited
Week 6 (10/31)
A Brief Introduction to Unbounded Linear Operators
The Closed Range Theorem
Week 7 (11/7)
Weak Topology
The properties of Weak Topology
Week 8 (11/14)
Weak* Topology
Weak Compactnes
Week 9 (11/21)
Reflexive Spaces
Week 10 (11/28)
A Brief Introduction to Convex Analysis (VI)
Week 11 (12/5)
The Baire Category Theorem
Week 12 (12/12)
The Uniform Boundedness Principle (I)
Week 13 (12/19)
The Uniform Boundedness Principle (II)
Week 14 (12/26)
The Open Mapping Theorem and the Closed Graph Theorem (I)
Week 15 (1/2)
The Open Mapping Theorem and the Closed Graph Theorem (II)
Week 16 (1/9)
Complementary Subspaces and Orthogonality Revisited (I)
Week 17 (1/16)
Complementary Subspaces and Orthogonality Revisited (II)
Week 18 (1/23)
Complementary Subspaces and Orthogonality Revisited (III)
Week 19 (1/30)
A Brief Introduction to Unbounded Linear Operators (I)
Reference：
1. Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis
2. Functional Analysis, Walter Rudin.
3. Variational Methods, Michael Struwe
Organizer: Chun-Hsiung Hsia (NTU)
