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General |
MATH 632 , Fall 2018: Notes and Summary
| Lecture | Date | What was covered | Notes | Textbook Section (R=Rudin; S=Simon) |
| 1 | Aug. 28 | Intro. to Functional Analysis | get assignment 1 | |
| 2 | Aug. 30 | Regularity of Topological Vector Spaces | - | (R)1.10 |
| 3 | Sep. 4 | Metrizability of Topological Vector Spaces | (R)1.24 | |
| 4 | Sep. 6 | Seminorms and Minkowski functional | return assignment 1 | (R)1.33-1.36 |
| 5 | Sept.11 | Induced Topology by seminorms | (R) 1.37-1.44 | |
| 6 | Sept.13 | C(Omega), Cinf(Omega) | get assignment 2 | (R) 1.44, 1.46 |
| 7 | Sept.18 | Baire Category theorem | (S1) 5.4 | |
| 8 | Sept.20 | Uniform boundedness principle (Banach-Steinhaus theorem), open mapping theorem | return assignment 2 | 5.4 |
| 9 | Sept.25 | Closed Graph Theorem, Hahn-Banach Theorem | (S1) 5.5 | |
| 10 | Sept.27 | Hahn-Banach and Separation | (S1) 5.5 | |
| 11 | Oct. 2 | Duals and Embeddings | (S1) 5.5 | |
| 12 | Oct. 4 | Quotient Space | ||
| 13 | Oct.9 | l1 and linf embeddings | ||
| 14 | Oct.11 | Banach-Alaoglu theorem | get assignment 3 | |
| 15 | Oct.16 | Embedding into continuous functions over the weak*unit ball. Density of the unit sphere. | ||
| 16 | Oct.18 | Weak Closure of convex sets | return assignment 3 | |
| - | Mon., Oct.22 | canceled | ||
| 17 | Oct.23 | Close Range Theorem/MID TERM EXAM | ||
| 18 | Oct.25 | Banach Algebras. Spectrum and Resolvent set | ||
| 19 | Oct.30 | Vector-Valued Integration | ||
| 20 | Nov. 1 | Weak holomorphy and holomorphy for Banach space vector-valued functions | ||
| 21 | Nov. 6 | Gelfand Formula for spectral radius | ||
| 22 | Nov. 8 | Holomorphic Functional Calculus | get assignment 4 | |
| 23 | Nov.13 | Spectral Mapping Theorem for Holomorphic Functional Calculus | ||
| 24 | Nov.15 | Spectral Localization. Quasi-Nilpotents | ||
| 25 | Nov.20 | Square Root Lemma | ||
| - | Nov.22 | THANKSGIVING BREAK | NO CLASS | |
| 26 | Nov.27 | Polar Decomposition | return assignment 4 | |
| 27 | Nov.29 | Continuous Resolutions of Identity; Integral formulas with respect to PVM | get assignment 5 | |
| 28 | Dec. 4 | No class | ||
| 29 | Dec. 6 | Spectral theorem | return assignment 5 | |
| - | Friday, Dec. 7 | Spectral theorem (2) / Review Session | 1:30pm-3:30pm | CSIC 4122 |
| - | TBD | FINAL EXAM | TBD | TBD |
