Basic Methods of Linear Functional Analysis (Dover Books on Mathematics)

An introduction to the themes of mathematical analysis, this text is geared toward advanced undergraduate and graduate students. It assumes a familiarity with basic real analysis, metric space theory, linear algebra, and minimal knowledge of measures and Lebesgue integration, all of which are surveyed in the first chapter.
Subsequent chapters explore the basic results of linear functional analysis: Stone-Weierstrass, Hahn-Banach, uniform boundedness and open mapping theorems, dual spaces, and basic properties of operators. Additional topics include function spaces, the Tychonov and Alaoglu theorems, Hilbert spaces, elementary Fourier analysis, and compact self-adjoint operators applied to Sturm-Liouville theory. "The author has a delightfully lively style which makes the book very readable," noted the Edinburgh Mathematical Society, "and there are numerous interesting and instructive problems."