Basic topological concepts, Metric spaces, Normed linear spaces, Banach spaces,
Bounded linear functionals and dual spaces,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.
Goffman, C. and Pedrick, G., First Course in Functional Analysis, Prentice-
Hall of India, 1995.
Rudin, W., Functional Anaysis, 2nd Edition, Tata McGraw-Hill, 2006
Yosida, K., Functional Anaysis, 4th Edition, Narosa,1974