MTH 732 (Fall 2023): Functional Analysis II

Instructor: Hanfeng Li

Office Hours: W 2-3pm

Lectures: TR 11:00am-12:20pm

Room: 235 Math Building

Course Description

This is the second semester of a one-year course. The theory of operator algebras (including C*-algebras and von Neumann algebras) grew out of the development of quntum mechnics, but now has interaction with many areas of mathematics.  We shall develop first the basic theory of C*-algebras (spectrum, functional calculus, positive elements, approximate units, states, GNS construction, ideals, homomorphisms, etc.), and discuss some important examples, including AF algebras, Cuntz algebras (more generally, Cuntz-Krieger algebras), and noncommutative tori (more generally, twisted group C*-algberas), coming from mathematical physics, dynamics, and group representations.

Recommended Reading
         The standard references for C*-algebra theory include:
           C*-algebras     by Dixmier,
           C*-algebras and W*-algebras     by Sakai,
           An invitation to C*-algebras     by Arveson,
           C*-algebras and their Automorphism Groups    by Pedersen,
           C*-algebras and Operator Theory    by Murphy,
           Fundamentals of the Theory of Operator Algebras    by Kadison and Ringrose,
           C*-algebras by Example    by Davidson,
           Theory of Operator Algebras    by Takesaki.
         We shall not follow closely any of these books.

Prerequisite

MTH 731: Functional Analysis I.