Course Archives Theoretical Statistics and Mathematics Unit
Course: Advanced Functional Analysis
Level: Postgraduate
Time: Currently not offered
Syllabus
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).
Top of the page

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

Top of the page

[ Semester Schedule ][ SMU ] [Indian Statistical Institute]