Functional Analysis I

Catalog description

Topological vector spaces; locally convex spaces (Hahn-Banach Theorem, weak topology, dual pairs, Krein-Milman Theorem, theory of distributions); Banach spaces (Uniform Boundedness Principle, Open Mapping Theorem and applications, Alaoglu's Theorem, analytic vector-valued functions, Krein-Smulian Theorem); C(X) as a Banach space (Stone-Weierstrass Theorem, Riesz Theorem); Lp spaces.