Integrated MSc-PhD Program

SYLLABUS

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. 1. 1. 1. 1. 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