Topics in Functional Analysis (MAA7527)

Spring 2020: MWF 6th hour, Little Hall, room 223


Office: Little Hall 480

Office Hours: By appointment

Course Content

Prerequisites: MAA 6616-7 (Measure Theory and Functional Analysis) or consent of the instructor.

Topics: The course is a continuation of 7526, with a focus on developing multivariable operator theory. This course will serve as an introduction to the theory of linear operators on Hilbert space. One main goal will be to understand the relationship between complex analysis and operator theory. Topics covered will include: Sz-Nagy dilation, von Neumann inequality, Pick interpolation, Herglotz and Nevanlinna representations, spectral theory for unbounded self-adjoint operators, perturbation theory, moment problems and so on. The main goal for the first section of the course will be to prove the Nevanlinna representation. We will encounter many important objects and big theorems as we proceed on this quest.

Texts: No text is required.  Peter Lax “Functional Analysis” is recommended.

In addition I will suggest homework problems and exercises which will be posted here and occasionally discussed in lecture.


Grading policies

Grading will be based on attendance and participation. Additionally, each member of the class, (excluding members of the class that presented last semester) must give at least one presentation either in class or the Analysis seminar on a topic of interest to complete the course.


Additional Information:


Grading will be in accord with the UF policy stated at

Academic Honesty

The course will be conducted in accordance with the University honor code and academic honesty policy, which can be found in the

student guide

Accommodation for students with disabilities.

“Students with disabilities requesting accommodations should first register with the Disability Resource Center(352-392-8565,

) by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester.”

Online Evaluations.

“Students are expected to provide feedback on the quality of instruction in this course by completing online evaluations at

. Evaluations are typically open during the last two or three weeks of the semester, but students will be given specific times when they are open. Summary results of these assessments are available to students at”

Contact information for the Counseling and Wellness Center.