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:
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