This excellent book provides an elegant
introduction to functional analysis … carefully selected problems
… This is a nicely written book of great value for stimulating
active work by students. It can be strongly recommended as an
undergraduate or graduate text, or as a comprehensive book for
self-study.
—European Mathematical Society Newsletter
Functional analysis plays a crucial role in the applied sciences as
well as in mathematics. It is a beautiful subject that can be
motivated and studied for its own sake. In keeping with this basic
philosophy, the author has made this introductory text accessible to a
wide spectrum of students, including beginning-level graduates and
advanced undergraduates. The exposition is inviting, following threads
of ideas, describing each as fully as possible, before moving on to a
new topic. Supporting material is introduced as appropriate, and only
to the degree needed. Some topics are treated more than once,
according to the different contexts in which they arise. The
prerequisites are minimal, requiring little more than advanced
calculus and no measure theory. The text focuses on normed vector
spaces and their important examples, Banach spaces and Hilbert
spaces. The author also includes topics not usually found in texts on
the subject.
This Second Edition incorporates many new developments while not
overshadowing the book's original flavor. Areas in the book that
demonstrate its unique character have been strengthened. In
particular, new material concerning Fredholm and semi-Fredholm
operators is introduced, requiring minimal effort as the necessary
machinery was already in place. Several new topics are presented, but
relate to only those concepts and methods emanating from other parts
of the book. These topics include perturbation classes, measures of
noncompactness, strictly singular operators, and operator
constants. Overall, the presentation has been refined, clarified, and
simplified, and many new problems have been added. The book is
recommended to advanced undergraduates, graduate students, and pure
and applied research mathematicians interested in functional analysis
and operator theory.
Readership
Advanced undergraduates, graduate students, and pure and applied
research mathematicians interested in functional analysis and operator theory.