FROM THE

PREFACE TO THE

FIRST EDITION

Because of the crucial role played by functional analysis in the applied sci-

ences as well as in mathematics, I have attempted to make this book ac-

cessible to as wide a spectrum of beginning students as possible. Much of

the book can be understood by a student having taken a course in advanced

calculus. However, in several chapters an elementary knowledge of functions

of a complex variable is required. These include Chapters 6, 9, and 11. Only

rudimentary topological or algebraic concepts are used. They are introduced

and proved as needed. No measure theory is employed or mentioned.

The book is intended for a one-year course for beginning graduate or

senior undergraduate students. However, it can be used at any level where

the students have the prerequisites mentioned above.

I have restricted my attention to normed vector spaces and their impor-

tant examples, Banach and Hilbert spaces. These are venerable institutions

upon which every scientist can rely throughout his or her career. They are

presently the more important spaces met in daily life. Another considera-

tion is the fact that an abundance of types of spaces can be an extremely

confusing situation to a beginner.

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