Integrated MSc-PhD Program

SYLLABUS

KSM3E01: Functional Analysis

Normed linear spaces, Banach spaces, Bounded linear functionals, dual spaces and weak topologies, Hahn-Banach theorem, Bounded linear operators, open-mapping theorem, closed graph theorem. The Banach-Steinhaus theorem, Hilbert spaces, Riesz representation theorem, orthogonal complements, bounded operators on a Hilbert space up to (and including) the spectral theorem for compact, self-adjoint operators.

Suggested texts:

1. 1. 1. 1. 1. 1. Rudin, Functional Analysis (2nd Ed.), McGraw-Hill, 2006.
               2. Yosida, K., Functional Analysis (4th Edition), Narosa, 1974.
               3. Conway, Functional analysis