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C* algebras and spectral theorem

Offered By: Indian Institute of Science Bangalore via Swayam

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Algebra Courses Functional Analysis Courses Spectral Theory Courses Banach Algebra Courses C* algebras Courses

Course Description

Overview

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

Taught by

Prof. E. K. Narayanan

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