MATH 656: FUNCTIONAL ANALYSIS II
SPRING 2016
Instructor: Michael Brannan, 502B Blocker, mbrannan@math.tamu.edu.
Lectures: TR 11:10am - 12:25pm, 624 Blocker.
Office Hours: Monday-Friday, by appointment.
Course Webpage: http://www.math.tamu.edu/˜mbrannan/math656/
Course Description: This course is intended to be a first introduction to Banach algebras
and operator algebras. The tentative plan for the course is as follows:
• Elementary Banach algebra theory: Basic definitions and examples, the functional
calculus, the spectrum.
• Abelian Banach algebras: The Gelfand transform, the radical.
• C∗ -Algebras: Definitions and basic theory, ideals, states, the Gelfand-Naimark thoerem, the GNS construction.
• The spectral theorem for normal operators on Hilbert space.
• Von Neumann algebras: The double commutant theorem, Kaplansky’s density theorem, abelian von Neumann algebras.
• One or more of the following topics (time permitting): Group C∗ -algebras, tensor
products of C∗ -algebras and nuclearity, amenability, . . .
Textbook: There is no required textbook for this course. However, good general references
include “C∗ -algebras and operator theory” by Gerard J. Murphy, “C∗ -algebras by example”
by Kenneth R. Davidson, and “An invitation to C∗ -algebras” by William Arveson.
Student Evaluation:
• 60 %–Homework assignments (approx. 4).
• 40 %–Informal class presentation on a topic related to the course material. The
student will also submit short written summary of their presentation topic. Specific
presentation topics will be posted on the course webpage at a later date. Students are
welcome to choose their own topic, provided the instructor deems the topic suitable.
1