MSM1401 - Functional Analysis-II

M.SC. MATHEMATICS SEMESTER – 4

MSM1401 – FUNCTIONAL ANALYSIS – II

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 Papers :

• April/May 2012

• April/May 2013

• March/April 2014

• April/May 2018

• April/May 2019

• March/April 2020 (MCQ Base Online Exam held in 19/09/2020)