C* algebras and spectral theorem
INTENDED AUDIENCE :MSc 2nd year , PhD students and college lecturers
PREREQUISITES : First course in functional analysis is a must. See http://math.iisc.ac.in/all-courses/ma223.html
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 properties
Prof. E. K. Narayanan
IISc Bangalore
I am a professor at the Department of Mathematics, Indian Institute of Science, Bangalore. My primary research area is harmonic analysis.
Course layout
Week 1: Review of finite dimensional spectral theorem
Week 2: Review of spectral theorem for compact normal operators
Week 3: Banach algebras
Week 4: C* algebras
Week 5: Gelfand-Naimark Theorem
Week 6: Projection valued measures
Week 7: Spectral theorem
Week 8: Spectral theory of * representations
Books and references
W. Rudin : Functional Analysis
G. B. Folland: bstract armonic analysis (first chapter)
R. G. Douglas: Banach algebra techniques in operator theory
