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Winter 2009 Math 646

What, When, and Where:

Course Description:

Functional Analysis and Applications

Text:

Cover of "Graduate Texts in Mathematics: A Course in Functional Analysis, Second Edition" by John B. Conway

Lectures:

TuTh 9:30-10:45a 126 TMCB

Office Hours:

TuTh 5:00-5:50p 306 TMCB

Grading Scheme:

100% Homework Assignments

Course Schedule: (subject to change)

Jan 13 Topology Review
Jan 15 Weak and weak-* topologies
Jan 20 Banach-Alaoglu Theorem
Jan 22 Duals and Convexity
Jan 27 Reflexive Spaces
Jan 29 Krein-Milman theorem
Feb 03 Stone Weierstrass Theorem
Feb 05 Adjoint Operators on a Banach Space
Feb 10 Compact Operators on a Banach Space
Feb 12 Compact Operators on a Banach Space
Feb 17 No Class--Holiday
Feb 19 Ascoli-Arzela and Finite Rank Operators
Feb 24 Banach Algebras I
Feb 26 Banach Algebras I
Mar 03 Resolvent Calculus I
Mar 05 Resolvent Calculus II
Mar 10 Resolvent Calculus III
Mar 12 Spectrum in a Banach Algebra I
Mar 17 Schecter Talk
Mar 19 Spectrum in a Banach Algebra II

Assignments:

Assignment #1 4.3 # 3,5,7 and 5.1 # 9,10
Assignment #2 6.1 # 1,6 and 6.3 # 1,2,4