PREFACE TO THE
The ﬁrst edition of Principles of Functional Analysis enjoyed a successful
run of 28 years. In revising the text, we were confronted with a dilemma.
On the one hand, we wanted to incorporate many new developments, but
on the other, we did not want to smother the original flavor of the book.
As one usually does under such circumstances, we settled for a compromise.
We considered only new material related to the original topics or material
that can be developed by means of techniques existing within the original
framework. In particular, we restricted ourselves to normed vector spaces
and linear operators acting between them. (Other topics will have to wait
for further volumes.) Moreover, we have chosen topics not readily available
in other texts.
We added sections to Chapters 3, 5, 7, 9, and 13 and inserted a new
chapter – Chapter 14. (The old Chapter 14 now becomes Chapter 15.)
Added topics include products of operators (Sections 5.7 and 7.7), a more
general theory of semi-Fredholm operators (Sections 5.6 and 7.6), Riesz op-
erators (Section 9.6), Fredholm and semi-Fredholm perturbations (Sections
9.6 and 9.7), spectral theory for unbounded selfadjoint operators (Section
13.6), and measures of operators and perturbation functions (Chapter 14).
We attempted to strengthen those areas in the book that demonstrate
its unique character. In particular, new material introduced concerning
Fredholm and semi-Fredholm operators requires minimal eﬀort since the