Basic Functional Analysis

Undergraduate / Graduate

Review of metric spaces, normed spaces and inner product spaces. Banach spaces and Hilbert spaces. Bounded linear operators. The 3 basic principles of functional analysis: the closed graph theorem, the open mapping theorem and the uniform boundedness principle. Duality and weak topologies. Weak and weak star compactness. Hilbert spaces, orthogonal expansions and spectral theorem. Applications of these concepts.