This book introduces the reader to the basic principles of functional
analysis and to areas of Banach space theory that are close to nonlinear
analysis and topology. In the first part, the book develops the
classical theory, including weak topologies, locally convex spaces,
Schauder bases, and compact operator theory. The presentation is
self-contained, including many folklore results, and the proofs are
accessible to students with the usual background in real analysis and
topology. The second part covers topics in convexity and smoothness,
finite representability, variational principles, homeomorphisms, weak
compactness and more. Several results are published here for the first
time in a monograph. The text can be used in graduate courses or for
independent study. It includes a large number of exercises of different
levels of difficulty, accompanied by hints. The book is also directed to
young researchers in functional analysis and can serve as a reference
book.This is an introduction to basic principles of functional analysis
and to areas of Banach space theory close to nonlinear analysis and
topology. The first part, which develops the classical theory, is
self-contained and features a large number of exercises containing many
important results. The second part covers selected topics in the theory
of Banach spaces related to smoothness and topology. It is intended to
be an introduction to and complement of existing books on the subject.
This text may be used in graduate courses, for independent study, or as
a reference book.
