**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Normed Vector spaces, Banach spaces with particular examples(lp spaces), Hilbert spaces-orthogonality and geometric structure, projections.
- Bounded linear functionals and dual of a normed vector space including duals of , .
- Riesz representation theorem for Hilbert spaces and applications, existence of maximal orthonormal set in a Hibert space
- Hahn Banach theorem, open mapping theorem, closed graph theorem, Banach-Steinhaus theorem.
- Bounded operators on a Hilbert space, Compact operators with particular examples like integral kernel operators, spectral theorem of compact symmetric operators on a Hilbert Space
- Hilbert spaces, orthogonality and geometric structure, projections, Reisz representation theorem.

Additional Topics Weak topology, Banach-Alaoglu theorem, Spectrum of a bounded
operator, Riesz functional calculus

- W. Rudin: Real and complex Analysis
- J. B. Conway: First course in Functional Analysis,
- C. Goffman and G. Pedrick: A first course in Functional Analysis,
- K. Yoshida: Functional Analysis