Course Archives Theoretical Statistics and Mathematics Unit
Course: Advanced Functional Analysis
Instructor: T S S R K Rao
Room: G25
Level: Postgraduate
Time: Currently offered
Past Exams

Syllabus: Brief introduction to topological vector spaces (TVS) and locally convex TVS. Linear Operators. Uniform Boundedness Principle. Geometric Hahn-Banach theorem and applications (Markov- Kakutani xed point theorem, Haar Measure on locally compact abelian groups, Liapounovs theorem). Extreme points and Krein-Milman theorem. In addition, one of the following topics:
(a) Geometry of Banach spaces: vector measures, Radon-Nikodym Property and geometric equivalents. Choquet theory. Weak compactness and Eberlein- Smulian Theorem. Schauder Basis.
(b) Banach algebras,spectral radius, maximal ideal space, Gelfand transform.
(c) Unbounded operators, Domains, Graphs, Adjoints, spectral theorem.

Suggested Texts :
1. N. Dunford and J. T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers, John Wiley (1963).
2. Walter Rudin, Functional analysis Second edition, International Series in Pure and Applied Mathematics. McGraw-Hill (1991).
3. K. Yosida, Functional analysis, Springer (Indian reprint 2004).
4. J. Diestel and J. J. Uhl, Jr., Vector measures, Mathematical Surveys (15), AMS (1977).

Midterm Exam 40 marks
Assignment -- marks
Final Exam 60 marks
Total 100 marks

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Past Exams
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11.pdf 15.pdf 17.pdf
Supplementary and Back Paper
11.pdf 15.pdf 17.pdf

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