C* algebras and spectral theorem

By Prof. E. K. Narayanan   |   IISc Bangalore
Learners enrolled: 116
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
Course Status : Upcoming
Course Type : Elective
Duration : 8 weeks
Start Date : 20 Feb 2023
End Date : 14 Apr 2023
Exam Date : 30 Apr 2023 IST
Enrollment Ends : 20 Feb 2023
Category :
  • Mathematics
Credit Points : 2
Level : Postgraduate

Page Visits

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

Instructor bio

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 certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 30 April 2023 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IISc Bangalore. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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