Course11110816440 lectures

C* Algebras and Spectral Theorem

Prof. E K Narayanan · IISc Bangalore

About

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

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

Lectures

Week 1 Spectral theorem For compact operators

Week 2 Banach algebras and Gelfand transform

Week 3 Gelfand-Naimark theorem

Week 4 Gelfand-Naimark theorem And functional calculus

Week 5 Spectral theorem for commutative C* sub algebras Of operators

Week 6 Spectral theorem and Resolution of identity

Week 7 Equivalence of various forms of spectral theorems And commuting families

Week 8 Spectral theorem for a commuting family of Normal operators

Syllabus and materials

At NPTEL, as the course publishes them.

Syllabus

Credits and licence

Institution: IISc Bangalore
Department: Mathematics
Teacher: Prof. E K Narayanan
Level: Graduate
Language: English
Subjects: Mathematics
Source: NPTEL
Licence: CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution: NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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