This concise textbook states and proves all of the major theorems of Banach space theory, locally convex space theory, Hilbert space theory, and spectral theory-presenting results in the most commonly used form, which enables the reader to concentrate on the prominent points of the argument and concepts.

Containing exercises designed for students to practice the technique shown in the proofs as well as to clarify elaborate arguments, FUNCTIONAL ANALYSIS defines and studies the familiar classes of operators including compact, Hilbert-Schmidt, trace class, and selfadjoint in terms of their spectral representations ... explores the axiomatic approach to experimental science and motivates the development of spectral theory as a model of those axioms ... describes the basic results on infinite-dimensional calculus, preparing the reader to study analysis on manifolds ... details the aspects of general topology most critical to functional analysis ... and more.

Appropriate for students with a prerequisite course in general measure theory, FUNCTIONAL ANALYSIS serves as an excellent primary text for graduate students taking such two-semester courses as Functional Analysis, Topological Vector Spaces, Spectral Theory, Hilbert Spaces, and Banach Spaces.

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