Normed linear spaces and continuous linear transformations, Hahn-Banach theorem (analytic and geometric versions), Baire’s theorem and its consequences – three basic principles of functional analysis (open mapping theorem, closed graph theorem and uniform boundedness principle), Computing the dual of wellknown Banach spaces, Hilbert spaces, Riesz representation theorem, Adjoint operator, Compact operators, Spectral theorem for self adjoint compact operators.
- J. B. Conway, “A Course in Functional Analysis”, Graduates Texts in Mathematics 96, Springer, 2006.
- B. Bollob ́as, “Linear Analysis”, Cambridge University Press, 1999.
- G. F. Simmons, “Introduction to Topology and Modern Analysis”, Tata McGraw- Hill, 2013.