Graduate students in mathematics, who want to travel light, will find this book invaluable; impatient young researchers in other fields will enjoy it as an instant reference to the highlights of modern analysis. Starting with general topology, it moves on to normed and seminormed linear spaces. From there it gives an introduction to the general theory of operators on Hilbert space, followed by a detailed exposition of the various forms the spectral theorem may take; from Gelfand theory, via spectral measures, to maximal commutative von Neumann algebras. The book concludes with two supplementary chapters: a concise account of unbounded operators and their spectral theory, and a complete course in measure and integration theory from an advanced point of view.
Nicely produced text for graduate students, derived from a course on the "fundamentals of functional analysis" given at the University of Copenhagen in 1982/83, and intended to provide review of "what every young analyst should know". The six chapters treat general topology, Banach spaces, Hilbert spaces, spectral theory, unbounded operators, integration theory. Discussion of conceptual/methodological material is brief and to the point, and much space is given to the exercises. Useful contribution to the advanced pedagogical literature. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)