Math 241B (Functional Analysis)

Math 241B (Driver, Winter 2020) Functional Analysis

(http://www.math.ucsd.edu/~bdriver/241B_W2020/index.htm)

## Announcements

 Last two lectures are in this file:  Lecture Notes/241_Lectures on QM.pdf See 241Functional_2020_Ver5.pdf for the newest version of the lecture notes. See suggested homework problems at: Homeworks/241b_Exercise1.pdf.

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 TuTh 8:00a - 9:20a in AP&M 2402

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 and basic knowledge of  Banach and Hilbert spaces is necessary!

Grading: Your course grade will be based on attendance and possible short presentation to the class about a homework problem or topic of interest.

Course Description:  This two quarter course is an introduction to Functional Analysis. The rough plan for Math 241B is to cover in various amounts of detail the following topics (which are subject to change):

1.  Banach Algebras:
1.  Linear ODE's
2. Spectral Theory of single elements
3. Holomorphic functional calculus.
4. Spectral theory and Spectral theorem for a self-adjoint operator.

2.  C*-algebras.
1. Basic properties and examples.
2. Structure of commutative C* - algebras and the spectral theorem, i.e.  simultaneous diagonalization of commuting normal operators.

3.  Unbounded operators.
1. Basic definitions and properties.
2. Some examples of unbounded operators coming from differential operators.
3. Contraction semi-groups and the Hille-Yosida Theorem