HNGU M.SC. MATHEMATICS SEMESTER - 4
MSM1401 β FUNCTIONAL ANALYSIS - 2
Unit 1:
- Dual and transpose of a Hilbert spaces
- Adjoint of an operator
- Self-adjoint, normal
- Unitary operators
- Projections
Unit 2:
- Finite dimensional spectral theorem
- Weak convergence
Unit 3:
- Banach algebra: definition and examples
- Regular and singular elements
- Topological divisiors of zero
- Spectral of an element and spectral radius
- Radical and simplicity
Unit 4:
- Gelfand mapping
- Applications of the formula of the spectral radius
- involutions in Banach algebra
- Ideals in C(X), Banach-Stone theorem
- Commutative C*-algebras.
Download Reference Books:
Note: The course is roughly covered by the following books:
Introduction to Topology and Modern Analysis - G. F. Simmons, McGraw Hill,1963.
1. Functional Analysis 2nd Edition - B. V. Limaye, New Age International Limited, 2nd edition.
2. Banach Algebra - R Larson, Marcell Dekker,1973.
3. Automatic Continuity - H G Dales, Cambridge, 2000
4. Lectures in Functional Analysis and Operator theory - S. K. Berberain, Springer Verlag.
5. First course in Functional Analysis - Goffman and George Padre, Prentice Hall of India.
6. Principles of Functional Analysis - Martin Schechter, Academic Press, New York.
| OLD Question Paper | |
|---|---|
| May/June - 2012 | Download |
| Nov/Dec - 2014 | Download |
| Nov/Dec - 2015 | Download |
| Nov/Dec - 2016 | Download |
| May/June - 2017 | Download |
| Nov/Dec - 2018 | Download |
| Nov/Dec - 2019 | Download |
| Nov/Dec - 2020 (MCQ) | Download |
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