Course Archives Theoretical Statistics and Mathematics Unit | |||||||||
Course: Advanced Functional Analysis Level: Postgraduate Time: Currently not offered |
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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 | |||||||||
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