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)1.331.36 
5 
Sept.11 
Induced Topology by seminorms 

(R) 1.371.44 
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 (BanachSteinhaus theorem), open mapping theorem 
return assignment 2 
5.4 
9 
Sept.25 
Closed Graph Theorem, HahnBanach Theorem 

(S1) 5.5 
10 
Sept.27 
HahnBanach 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 
BanachAlaoglu 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 
11:00am1:00pm 
canceled 
17 
Oct.23 
Close Range Theorem/MID TERM EXAM 


18 
Oct.25 
Banach Algebras. Spectrum and Resolvent set 


19 
Oct.30 
VectorValued Integration 


20 
Nov. 1 
Weak holomorphy and holomorphy for Banach space vectorvalued 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. QuasiNilpotents 


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 
1:30pm3:30pm 
CSIC 4122 
 
TBD 
FINAL EXAM 
TBD 
TBD 