BASIC METHODS OF LINEAR
FUNCTIONAL ANALYSIS

This book is intended for final year honours undergraduates of first-year graduates and develops the basic results of linear functional analysis (Stone-Weierstrass, Hahn-Banach, uniform boundedness and open-mapping theorems, dual spaces and basic properties of operators), assuming some knowledge of topology and Lebesque integration and with a geometrical slant. Ther are also sections on function spaces, the Tychonov and Alaoglu theorems, Hilbert spaces, elementary Fourier analysis, and compact self-adjoint operators applied to Sturm-Liouville theory.