Arnold D.N. Functional Analysis

1997. — 37 pages.These lecture notes were prepared for the instructor's personal use in teaching a half-semester course on functional analysis at the beginning graduate level at Penn State, in Spring 1997.Vector spaces and their topology (Subspaces and quotient spaces; Basic properties of Hilbert spaces)
Linear Operators and Functionals (The Hahn-Banach Theorem; Duality)
Fundamental Theorems (The Open Mapping; Theorem; The Uniform Boundedness Principle;
The Closed Range Theorem)
Weak Topologies
Compact Operators and their Spectra (Hilbert-Schmidt operators, Compact operators,
Spectral Theorem for compact self-adjoint operators, The spectrum of a general compact operator)
Introduction to General Spectral Theory (The spectrum and resolvent in a Banach algebra,
Spectral Theorem for bounded self-adjoint operators)