Details of MA5203 (Spring 2022)
| Level: 5 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA5203 | Topics in Operator Theory | Shibananda Biswas |
| Syllabus |
|---|
| Operators on Hilbert Spaces: Projections and subspaces, commutative C*-algebras,
spectral theorem, continuous functional calculus, square root of positive operator, unilateral shift C*-algebras, noncommutative states and representations, Gelfand-Neumark representation theorem. Banach Algebras: Banach algebras, spectral radius, maximal ideal space, Gelfand transform. Spectral Theory of Normal Operators: Von-Neumann algebras, projections, double commutant theorem, L functional calculus. If time permits, one may choose from the following: Fredholm Theory: Compact operators on Hilbert Spaces, Fredholm theory, index. Unbounded Operators: Unbounded operators, domains, graphs, adjoints, spectral theorem. |
| Prerequisite |
|---|
| Complex Analysis (MA4201) and Functional Analysis (MA4102) |
| References |
|---|
| Suggested Texts:
1. Arveson, W., An Invitation to C*-algebras, Springer-Verlag. 2. Arveson, W., A Short Course in Spectral Theory, Springer-Verlag. 3. Conway, J.B., A Course in Operator Theory, American Mathematical Society. 4. Davidson, K., C*-algebras by Example, Fields Institute Monograph, AMS. 5. Douglas, R.G., Banach Algebra Techniques in Operator Theory, Springer. 6. Kadison, R.V. and Ringrose, J.R., Fundamentals of the Theory of Operator Algebras Vol. I. Elementary Theory, American Mathematical Society. 7. Murphy, G., C*-algebras and Operator Theory, Academic Press. 8. Rudin, W., Functional Analysis, Second edition, Tata McGraw-Hill. 9. Sunder, V.S., Functional Analysis: Spectral Theory, Hindustan Book Agency. 10. Zhu, K., Operator Algebras, Birkhauser. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Not Allowed |
| 5 | MP | 4 | Not Allowed |
| 6 | MR | 2 | Not Allowed |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 10 | Elective |
| 9 | MS | 4 | Not Allowed |
| 10 | MS | 6 | Not Allowed |
| 11 | MS | 8 | Not Allowed |
| 12 | RS | 1 | Not Allowed |
| 13 | RS | 2 | Not Allowed |