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

*(http://www.math.ucsd.edu/~bdriver/241_2015-16/index.htm)*

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## 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:
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.