Math 241A - 241B (Driver, Fall 2015 - Winter 2016) Functional
Analysis
(http://www.math.ucsd.edu/~bdriver/241_2015-16/index.htm)
Announcements
Instructor: Bruce Driver (bdriver@math.ucsd.edu), 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:
http://link.springer.com/book/10.1007/978-1-4757-3828-5. There
will quite likely be supplementary lecture notes available on this Web-site as
well.
Prerequisites:
Course Description:
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.