缺點：不是一本嚴謹的書，錯誤很多。材料的選取，例如第七章有關Domain及range straightening theorem、Morse定理方面的定理，為必要納入高微的內容；第六章有關Rn中的微分，處理得太複雜，不易閱讀。
建議：自修的同學，不宜以它為閱本。陳金次老師
This book grew out of courses given over many years by the author to graduate students at the Courant Institute and is composed of thirty-seven chapters and three appendices. The first part of the book, comprising the first twenty-five chapters, is intended for use as a text for an introductory graduate course in functional analysis. It deals with such topics as (to mention only a few) normed linear spaces and their duals, Banach and Hilbert spaces, weak convergence, weak and weak∗ topologies, locally convex topologies and the Krein-Milman theorem, Banach algebras and compact operators. The second part of the book, which is intended for more advanced graduate students, deals with such topics as (to mention only a few) the spectral theory of several types of operators, and in particular, selfadjoint ones, semigroups of operators, groups of unitary operators, and scattering theory. The appendices are devoted to the Riesz-Kakutani representation theorem, the theory of distributions, and Zorn's lemma. What is attractive about the book is the interspersing of chapters on theory with chapters on applications of the theory to a variety of problems arising in various branches of mathematics. The book is well suited for graduate courses in functional analysis and useful for research mathematicians.
Reviewer: Faierman, Melvin [form MathSciNet]