Course Archives Theoretical Statistics and Mathematics Unit | ||||||||||||||||||||||||||||
Course: Functional Analysis Level: Postgraduate Time: Currently not offered |
||||||||||||||||||||||||||||
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:
Top of the page Past Exams | ||||||||||||||||||||||||||||
Top of the page | ||||||||||||||||||||||||||||
[ Semester Schedule ] [ SMU ] [Indian Statistical Institute] |