Integrated MSc-PhD Program


KSM4E02: Advanced Functional Analysis

Topics covered: Banach algebra of continuous functions, Banach algebra of operators, abstract Banach algebras, space of multiplicative linear functionals, maximal ideal spaces, Gelfand transform, Gelfand-Mazur theorem, Gelfand theorem for commutative Banach algebras, Stone-Weierstrass theorem, generalized Stone-Weierstrass theorem, algebra of bounded measurable functions, Gelfand-Naimark theorem, spectral theorem for C*-algebras, functional calculus.

Suggested texts:

            1. Banach Algebra Techniques in Operator Theory by Ronald G. Douglas
            2. An Invitation to C-Algebras* by W. B. Arveson
            3. Functional Analysis by V. S. Sunder
            4. C-Algebras and Operator Theory* by G.J. Murphy
            5. Functional Analysis by M. Reed and B. Simon
            6. Linear Operator, General Theory by N. Dunford and T. Schwartz