C* Algebras and Spectral Theorem

ABOUT THE COURSE: Aim is to prove the spectral theorem for bounded normal operators using C* algebras and projection valued measures. After review of spectral theorem for compact normal operators we will introduce Banach algebras, C* algebras and prove Gelfand-Naimark theorem. Spectral theorem will be proved after a detailed study of projection valued measures and their propertiesINTENDED AUDIENCE: MSc 2nd year , PhD students and college lecturersPREREQUISITES: First course in functional analysis is a must. See http://math.iisc.ac.in/all-courses/ma223.html

Syllabus

Week 1: Review of finite dimensional spectral theoremWeek 2:Review of spectral theorem for compact normal operatorsWeek 3:Banach algebrasWeek 4:C* algebrasWeek 5:Gelfand-Naimark TheoremWeek 6:Projection valued measuresWeek 7:Spectral theoremWeek 8:Spectral theory of * representations