This text is a self-contained introduction to the three main families that we encounter in
analysis ¿ metric spaces normed spaces and inner product spaces ¿ and to the operators that
transform objects in one into objects in another. With an emphasis on the fundamental
properties defining the spaces this book guides readers to a deeper understanding of analysis
and an appreciation of the field as the ¿science of functions.¿ Many important topics that are
rarely presented in an accessible way to undergraduate students are included such as
unconditional convergence of series Schauder bases for Banach spaces the dual of ¿p
topological isomorphisms the Spectral Theorem the Baire Category Theorem and the Uniform
Boundedness Principle. The text is constructed in such a way that instructors have the option
whether to include more advanced topics. Written in an appealing and accessible style Metrics
Norms Inner Products and Operator Theory is suitable for independent study or as the basis
for an undergraduate-level course. Instructors have several options for building a course
around the text depending on the level and interests of their students.Key features:Aimed at
students who have a basic knowledge of undergraduate real analysis. All of the required
background material is reviewed in the first chapter. Suitable for undergraduate-level courses
no familiarity with measure theory is required. Extensive exercises complement the text and
provide opportunities for learning by doing. A separate solutions manual is available for
instructors via the Birkhäuser website (www.springer.com 978-3-319-65321-1). Unique text
providing an undergraduate-level introduction to metrics norms inner products and their
associated operator theory.
