Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.
Metric Spaces. Normed Spaces; Banach Spaces. Inner Product Spaces; Hilbert Spaces. Fundamental Theorems for Normed and Banach Spaces. Further Applications: Banach Fixed Point Theorem. Spectral Theory of Linear Operators in Normed Spaces. Compact Linear Operators on Normed Spaces and Their Spectrum. Spectral Theory of Bounded Self-Adjoint Linear Operators. Unbounded Linear Operators in Hilbert Space. Unbounded Linear Operators in Quantum Mechanics. Appendices. References.