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 |
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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). Evaluation:
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Midterm
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