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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 REVIEW SESSION 11:00am-1:00pm 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