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Course: Functional Analysis Instructor: B V Rajarama Bhat Room: G25 Level: Postgraduate Time: Currently offered |
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Syllabus Past Exams Syllabus:
Normed linear spaces, Banach spaces. Bounded linear operators. Dual of a normed linear space. Hahn-Banach theorem, uniform boundedness principle, open mapping theorem,
closed graph theorem. Computing the dual of wellknown Banach spaces. Weak and weak* topologies, Banach-Alaoglu Theorem. The double dual.L^p spaces, Riesz
representation theorem for the space C[0,1].Hilbert spaces, adjoint operators, self-adjoint and normal operators, spectrum, spectral radius, analysis of the spectrum of a compact operator on a Banach space, spectral theorem for bounded self-adjoint operators. Time permitting: reflexivity; spectral theorem for normal and unitary operators. Suggested Texts : 1. W. Rudin, Real and complex analysis, McGraw-Hill (1987). 2. W. Rudin, Functional analysis, McGraw-Hill (1991). 3. J. B. Conway, A course in functional analysis, GTM (96), Springer (Indian reprint 2006). 4. K. Yosida, Functional analysis, Springer (Indian reprint 2004). Evaluation:
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Midterm
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