MTH401: (Functional Analysis)

        [Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

• 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 $\ell^p$, $L^p$.
• 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

Reference Texts:

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