Math 241 (Functional Analysis)

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UCSD Catalog

Math 241A - 241B (Driver, Fall 2015 - Winter 2016) Functional Analysis


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Instructor: Bruce Driver (, AP&M 5260, 534-2648.

Bruce Driver's Office Hours: (To be determined)  in AP&M 5260.

Meeting times: Lectures are on MWF 9:00a - 9:50a in AP&M 7421

Textbook:  A Course in Functional Analysis 2nd Edision, (Graduate Texts in Mathematics), Dec 1, 2010 by John B Conway . UCSD affiliates may get the first edition on line at:   There will quite likely be supplementary lecture notes available on this Web-site as well.            

Prerequisites:  The official prerequisite for this course is Math 240A-B-C (Graduate real analysis) or consent of instructor. You could get away with less but some knowledge of Lebesgue integration theory is highly desirable.

Grading: Your course grade will be based on attendance and completion of a very modest number of homework problems.

Course Description:  This two quarter course is an introduction to Functional Analysis. The rough plan for Math 241A is to try to cover the following chapters of Conway (the text for this course);

Chapter 1.     Hilbert Spaces
Chapter 2.     Operators on Hilbert Spaces
Chapter 3.     Banach Spaces
Chapter 6.     Linear Operators on Banach Spaces
Section on:    The spectral theorem for bounded operators.

Math 241B will continue on where we left off:

Chapter 9.     Normal Operators on Hilbert Space
Section on: Compact operators and the spectral theorem
Chapter 10.   Unbounded Operators
Chapter 7.     Banach Algebras and Spectral Theory for Operators on a Banach Space
Chapter 8.     C*-Algebras
Chapter 4.     Locally convex vector spaces
Chapter 5.     Weak topologies.

I plan on introducing unbounded operators fairly early in the course as they are more technically demanding and require considerable practice.  One of my main goals in Math 241A is to (at very least) introduce you to the spectral theorem for bounded and unbounded self-adjoint operators on Hilbert spaces. In 241B will cover topological vector spaces, fill in the missing details from 241A, along with various other topics. 


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Last modified on Tuesday, 15 September 2015 11:52 AM.