Functional analysis, partly because of its many applications, has become a very popular mathematical discipline. My own lectures on
the subject have been attended by applied mathematicians, prob-
abilists, classical and numerical analysts, arid even an algebraic
topologist. This book grew out of my attempts to present the
material in a way that was interesting and understandable to people with
such diverse backgrounds and professional goals. I have aimed at an
audience of professional mathematicians who want to learn some
functional analysis, and second-year graduate students who are
taking a course in the subject. The only background material needed is
what is usually covered in a one-year graduate level course in
analysis, and an acquaintance with linear algebra. The book is
designed to enable the reader to get actively involved in the
development of the mathematics. This can be done by working the starred
problems that appear at the end of nearly every section. I often refer
to these exercises during subsequent discussions and proofs.
Solutions to those starred problems appearing in the introductory
chapters (Chapters 1-4) can be found in Appendix A.