Cover; Title Page; Copyright Page; Preface; Contents; CHAPTER 1. Introduction to Inner Product Spaces; 1.1 Some Prerequisite Material and Conventions; 1.2 Inner Product Spaces; 1.3 Linear Functionals, the Riesz Representation Theorem, and Adjoints; Exercises 1; References; CHAPTER 2. Orthogonal Projections and the Spectral Theorem for Normal Transformations; 2.1 The Complexification; 2.2 Orthogonal Projections and Orthogonal Direct Sums; 2.3 Unitary and Orthogonal Transformations; Exercises 2; References; CHAPTER 3. Normed Spaces and Metric Spaces; 3.1 Norms and Normed Linear Spaces.

Excellent treatment of subject geared toward students with background in linear algebra, advanced calculus, physics and engineering. Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. Includes detailed proofs of theorems, bibliography, and index of symbols. 1966 edition.